Probability and statistics Books

Book SynopsisProbability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy. Unlike most books on probabilTable of ContentsPREFACE xxi NOTATION xxv 1 Overview and Background 1 1.1 Introduction 1 1.1.1 Signals, Signal Processing, and Communications 3 1.1.2 Probability, Random Variables, and Random Vectors 9 1.1.3 Random Sequences and Random Processes 11 1.1.4 Delta Functions 16 1.2 Deterministic Signals and Systems 19 1.2.1 Continuous Time 20 1.2.2 Discrete Time 25 1.2.3 Discrete-Time Filters 29 1.2.4 State-Space Realizations 32 1.3 Statistical Signal Processing with MATLAB® 35 1.3.1 Random Number Generation 35 1.3.2 Filtering 38 Problems 39 Further Reading 45 PART I Probability, Random Variables, and Expectation 2 Probability Theory 49 2.1 Introduction 49 2.2 Sets and Sample Spaces 50 2.3 Set Operations 54 2.4 Events and Fields 58 2.5 Summary of a Random Experiment 64 2.6 Measure Theory 64 2.7 Axioms of Probability 68 2.8 Basic Probability Results 69 2.9 Conditional Probability 71 2.10 Independence 73 2.11 Bayes’ Formula 74 2.12 Total Probability 76 2.13 Discrete Sample Spaces 79 2.14 Continuous Sample Spaces 83 2.15 Nonmeasurable Subsets of R 84 Problems 87 Further Reading 90 3 Random Variables 91 3.1 Introduction 91 3.2 Functions and Mappings 91 3.3 Distribution Function 96 3.4 Probability Mass Function 101 3.5 Probability Density Function 103 3.6 Mixed Distributions 104 3.7 Parametric Models for Random Variables 107 3.8 Continuous Random Variables 109 3.8.1 Gaussian Random Variable (Normal) 110 3.8.2 Log-Normal Random Variable 113 3.8.3 Inverse Gaussian Random Variable (Wald) 114 3.8.4 Exponential Random Variable (One-Sided) 116 3.8.5 Laplace Random Variable (Double-Sided Exponential) 119 3.8.6 Cauchy Random Variable 122 3.8.7 Continuous Uniform Random Variable 124 3.8.8 Triangular Random Variable 125 3.8.9 Rayleigh Random Variable 127 3.8.10 Rice Random Variable 129 3.8.11 Gamma Random Variable (Erlang for r ∈ N) 131 3.8.12 Beta Random Variable (Arcsine for α = β = 1/2, Power Function for β = 1) 133 3.8.13 Pareto Random Variable 136 3.8.14 Weibull Random Variable 137 3.8.15 Logistic Random Variable (Sigmoid for {μ = 0, α = 1}) 139 3.8.16 Chi Random Variable (Maxwell–Boltzmann, Half-Normal) 141 3.8.17 Chi-Square Random Variable 144 3.8.18 F-Distribution 147 3.8.19 Student’s t Distribution 149 3.8.20 Extreme Value Distribution (Type I: Gumbel) 150 3.9 Discrete Random Variables 151 3.9.1 Bernoulli Random Variable 152 3.9.2 Binomial Random Variable 154 3.9.3 Geometric Random Variable (with Support Z+ or N) 157 3.9.4 Negative Binomial Random Variable (Pascal) 160 3.9.5 Poisson Random Variable 162 3.9.6 Hypergeometric Random Variable 165 3.9.7 Discrete Uniform Random Variable 167 3.9.8 Logarithmic Random Variable (Log-Series) 168 3.9.9 Zeta Random Variable (Zipf) 170 Problems 173 Further Reading 176 4 Multiple Random Variables 177 4.1 Introduction 177 4.2 Random Variable Approximations 177 4.2.1 Binomial Approximation of Hypergeometric 177 4.2.2 Poisson Approximation of Binomial 179 4.2.3 Gaussian Approximations 181 4.2.4 Gaussian Approximation of Binomial 181 4.2.5 Gaussian Approximation of Poisson 181 4.2.6 Gaussian Approximation of Hypergeometric 183 4.3 Joint and Marginal Distributions 183 4.4 Independent Random Variables 186 4.5 Conditional Distribution 187 4.6 Random Vectors 190 4.6.1 Bivariate Uniform Distribution 193 4.6.2 Multivariate Gaussian Distribution 193 4.6.3 Multivariate Student’s t Distribution 196 4.6.4 Multinomial Distribution 197 4.6.5 Multivariate Hypergeometric Distribution 198 4.6.6 Bivariate Exponential Distributions 200 4.7 Generating Dependent Random Variables 201 4.8 Random Variable Transformations 205 4.8.1 Transformations of Discrete Random Variables 205 4.8.2 Transformations of Continuous Random Variables 207 4.9 Important Functions of Two Random Variables 218 4.9.1 Sum: Z = X + Y 218 4.9.2 Difference: Z = X − Y 220 4.9.3 Product: Z = XY 221 4.9.4 Quotient (Ratio): Z = X/Y 224 4.10 Transformations of Random Variable Families 226 4.10.1 Gaussian Transformations 226 4.10.2 Exponential Transformations 227 4.10.3 Chi-Square Transformations 228 4.11 Transformations of Random Vectors 229 4.12 Sample Mean ¯X and Sample Variance S2 232 4.13 Minimum, Maximum, and Order Statistics 234 4.14 Mixtures 238 Problems 240 Further Reading 243 5 Expectation and Moments 244 5.1 Introduction 244 5.2 Expectation and Integration 244 5.3 Indicator Random Variable 245 5.4 Simple Random Variable 246 5.5 Expectation for Discrete Sample Spaces 247 5.6 Expectation for Continuous Sample Spaces 250 5.7 Summary of Expectation 253 5.8 Functional View of the Mean 254 5.9 Properties of Expectation 255 5.10 Expectation of a Function 259 5.11 Characteristic Function 260 5.12 Conditional Expectation 265 5.13 Properties of Conditional Expectation 267 5.14 Location Parameters: Mean, Median, and Mode 276 5.15 Variance, Covariance, and Correlation 280 5.16 Functional View of the Variance 283 5.17 Expectation and the Indicator Function 284 5.18 Correlation Coefficients 285 5.19 Orthogonality 291 5.20 Correlation and Covariance Matrices 294 5.21 Higher Order Moments and Cumulants 296 5.22 Functional View of Skewness 302 5.23 Functional View of Kurtosis 303 5.24 Generating Functions 304 5.25 Fourth-Order Gaussian Moment 309 5.26 Expectations of Nonlinear Transformations 310 Problems 313 Further Reading 316 PART II Random Processes, Systems, and Parameter Estimation 6 Random Processes 319 6.1 Introduction 319 6.2 Characterizations of a Random Process 319 6.3 Consistency and Extension 324 6.4 Types of Random Processes 325 6.5 Stationarity 326 6.6 Independent and Identically Distributed 329 6.7 Independent Increments 331 6.8 Martingales 333 6.9 Markov Sequence 338 6.10 Markov Process 350 6.11 Random Sequences 352 6.11.1 Bernoulli Sequence 352 6.11.2 Bernoulli Scheme 352 6.11.3 Independent Sequences 353 6.11.4 Bernoulli Random Walk 354 6.11.5 Binomial Counting Sequence 356 6.12 Random Processes 359 6.12.1 Poisson Counting Process 359 6.12.2 Random Telegraph Signal 365 6.12.3 Wiener Process 368 6.12.4 Gaussian Process 371 6.12.5 Pulse Amplitude Modulation 372 6.12.6 Random Sine Signals 373 Problems 375 Further Reading 379 7 Stochastic Convergence, Calculus, and Decompositions 380 7.1 Introduction 380 7.2 Stochastic Convergence 380 7.3 Laws of Large Numbers 388 7.4 Central Limit Theorem 390 7.5 Stochastic Continuity 394 7.6 Derivatives and Integrals 404 7.7 Differential Equations 414 7.8 Difference Equations 422 7.9 Innovations and Mean-Square Predictability 423 7.10 Doob–Meyer Decomposition 428 7.11 Karhunen–Lo`eve Expansion 433 Problems 441 Further Reading 444 8 Systems, Noise, and Spectrum Estimation 445 8.1 Introduction 445 8.2 Correlation Revisited 445 8.3 Ergodicity 448 8.4 Eigenfunctions of RXX(τ ) 456 8.5 Power Spectral Density 457 8.6 Power Spectral Distribution 463 8.7 Cross-Power Spectral Density 465 8.8 Systems with Random Inputs 468 8.8.1 Nonlinear Systems 469 8.8.2 Linear Systems 471 8.9 Passband Signals 476 8.10 White Noise 479 8.11 Bandwidth 484 8.12 Spectrum Estimation 487 8.12.1 Periodogram 487 8.12.2 Smoothed Periodogram 493 8.12.3 Modified Periodogram 497 8.13 Parametric Models 500 8.13.1 Autoregressive Model 500 8.13.2 Moving-Average Model 505 8.13.3 Autoregressive Moving-Average Model 509 8.14 System Identification 513 Problems 515 Further Reading 518 9 Sufficient Statistics and Parameter Estimation 519 9.1 Introduction 519 9.2 Statistics 519 9.3 Sufficient Statistics 520 9.4 Minimal Sufficient Statistic 525 9.5 Exponential Families 528 9.6 Location-Scale Families 533 9.7 Complete Statistic 536 9.8 Rao–Blackwell Theorem 538 9.9 Lehmann–Scheff´e Theorem 540 9.10 Bayes Estimation 542 9.11 Mean-Square-Error Estimation 545 9.12 Mean-Absolute-Error Estimation 552 9.13 Orthogonality Condition 553 9.14 Properties of Estimators 555 9.14.1 Unbiased 555 9.14.2 Consistent 557 9.14.3 Efficient 559 9.15 Maximum A Posteriori Estimation 561 9.16 Maximum Likelihood Estimation 567 9.17 Likelihood Ratio Test 569 9.18 Expectation–Maximization Algorithm 570 9.19 Method of Moments 576 9.20 Least-Squares Estimation 577 9.21 Properties of LS Estimators 582 9.21.1 Minimum ξWLS 582 9.21.2 Uniqueness 582 9.21.3 Orthogonality 582 9.21.4 Unbiased 584 9.21.5 Covariance Matrix 584 9.21.6 Efficient: Achieves CRLB 585 9.21.7 BLU Estimator 585 9.22 Best Linear Unbiased Estimation 586 9.23 Properties of BLU Estimators 590 Problems 592 Further Reading 595 A Note on Part III of the Book 595 APPENDICES Introduction to Appendices 597 A Summaries of Univariate Parametric Distributions 599 A.1 Notation 599 A.2 Further Reading 600 A.3 Continuous Random Variables 601 A.3.1 Beta (Arcsine for α = β = 1/2, Power Function for β = 1) 601 A.3.2 Cauchy 602 A.3.3 Chi 603 A.3.4 Chi-Square 604 A.3.5 Exponential (Shifted by c) 605 A.3.6 Extreme Value (Type I: Gumbel) 606 A.3.7 F-Distribution 607 A.3.8 Gamma (Erlang for r ∈ N with (r ) = (r − 1)!) 608 A.3.9 Gaussian (Normal) 609 A.3.10 Half-Normal (Folded Normal) 610 A.3.11 Inverse Gaussian (Wald) 611 A.3.12 Laplace (Double-Sided Exponential) 612 A.3.13 Logistic (Sigmoid for {μ = 0, α = 1}) 613 A.3.14 Log-Normal 614 A.3.15 Maxwell–Boltzmann 615 A.3.16 Pareto 616 A.3.17 Rayleigh 617 A.3.18 Rice 618 A.3.19 Student’s t Distribution 619 A.3.20 Triangular 620 A.3.21 Uniform (Continuous) 621 A.3.22 Weibull 622 A.4 Discrete Random Variables 623 A.4.1 Bernoulli (with Support {0, 1}) 623 A.4.2 Bernoulli (Symmetric with Support {−1, 1}) 624 A.4.3 Binomial 625 A.4.4 Geometric (with Support Z+) 626 A.4.5 Geometric (Shifted with Support N) 627 A.4.6 Hypergeometric 628 A.4.7 Logarithmic (Log-Series) 629 A.4.8 Negative Binomial (Pascal) 630 A.4.9 Poisson 631 A.4.10 Uniform (Discrete) 632 A.4.11 Zeta (Zipf) 633 B Functions and Properties 634 B.1 Continuity and Bounded Variation 634 B.2 Supremum and Infimum 640 B.3 Order Notation 640 B.4 Floor and Ceiling Functions 641 B.5 Convex and Concave Functions 641 B.6 Even and Odd Functions 641 B.7 Signum Function 643 B.8 Dirac Delta Function 644 B.9 Kronecker Delta Function 645 B.10 Unit-Step Functions 646 B.11 Rectangle Functions 647 B.12 Triangle and Ramp Functions 647 B.13 Indicator Functions 648 B.14 Sinc Function 649 B.15 Logarithm Functions 650 B.16 Gamma Functions 651 B.17 Beta Functions 653 B.18 Bessel Functions 655 B.19 Q-Function and Error Functions 655 B.20 Marcum Q-Function 659 B.21 Zeta Function 659 B.22 Rising and Falling Factorials 660 B.23 Laguerre Polynomials 661 B.24 Hypergeometric Functions 662 B.25 Bernoulli Numbers 663 B.26 Harmonic Numbers 663 B.27 Euler–Mascheroni Constant 664 B.28 Dirichlet Function 664 Further Reading 664 C Frequency-Domain Transforms and Properties 665 C.1 Laplace Transform 665 C.2 Continuous-Time Fourier Transform 669 C.3 z-Transform 670 C.4 Discrete-Time Fourier Transform 676 Further Reading 677 D Integration and Integrals 678 D.1 Review of Riemann Integral 678 D.2 Riemann–Stieltjes Integral 681 D.3 Lebesgue Integral 684 D.4 Pdf Integrals 688 D.5 Indefinite and Definite Integrals 690 D.6 Integral Formulas 692 D.7 Double Integrals of Special Functions 692 Further Reading 696 E Identities and Infinite Series 697 E.1 Zero and Infinity 697 E.2 Minimum and Maximum 697 E.3 Trigonometric Identities 698 E.4 Stirling’s Formula 698 E.5 Taylor Series 699 E.6 Series Expansions and Closed-Form Sums 699 E.7 Vandermonde’s Identity 702 E.8 Pmf Sums and Functional Forms 703 E.9 Completing the Square 704 E.10 Summation by Parts 705 Further Reading 706 F Inequalities and Bounds for Expectations 707 F.1 Cauchy–Schwarz and H¨older Inequalities 707 F.2 Triangle and Minkowski Inequalities 708 F.3 Bienaym´e, Chebyshev, and Markov Inequalities 709 F.4 Chernoff’s Inequality 711 F.5 Jensen’s Inequality 713 F.6 Cram´er–Rao Inequality 714 Further Reading 718 G Matrix and Vector Properties 719 G.1 Basic Properties 719 G.2 Four Fundamental Subspaces 721 G.3 Eigendecomposition 722 G.4 LU, LDU, and Cholesky Decompositions 724 G.5 Jacobian Matrix and the Jacobian 726 G.6 Kronecker and Schur Products 728 G.7 Properties of Trace and Determinant 728 G.8 Matrix Inversion Lemma 729 G.9 Cauchy–Schwarz Inequality 730 G.10 Differentiation 730 G.11 Complex Differentiation 731 Further Reading 732 GLOSSARY 733 REFERENCES 743 INDEX 755 PART III Applications in Signal Processing and Communications Chapters at the Web Site www.wiley.com/go/randomprocesses 10 Communication Systems and Information Theory 771 10.1 Introduction 771 10.2 Transmitter 771 10.2.1 Sampling and Quantization 772 10.2.2 Channel Coding 777 10.2.3 Symbols and Pulse Shaping 778 10.2.4 Modulation 781 10.3 Transmission Channel 783 10.4 Receiver 786 10.4.1 Receive Filter 786 10.4.2 Demodulation 787 10.4.3 Gram–Schmidt Orthogonalization 789 10.4.4 Maximum Likelihood Detection 794 10.4.5 Matched Filter Receiver 797 10.4.6 Probability of Error 802 10.5 Information Theory 803 10.5.1 Mutual Information and Entropy 804 10.5.2 Properties of Mutual Information and Entropy 810 10.5.3 Continuous Distributions: Differential Entropy 813 10.5.4 Channel Capacity 818 10.5.5 AWGN Channel 820 Problems 821 Further Reading 824 11 Optimal Filtering www.wiley.com/go/randomprocesses 825 11.1 Introduction 825 11.2 Optimal Linear Filtering 825 11.3 Optimal Filter Applications 827 11.3.1 System Identification 827 11.3.2 Inverse Modeling 827 11.3.3 Noise Cancellation 828 11.3.4 Linear Prediction 828 11.4 Noncausal Wiener Filter 829 11.5 Causal Wiener Filter 831 11.6 Prewhitening Filter 837 11.7 FIR Wiener Filter 839 11.8 Kalman Filter 844 11.8.1 Evolution of the Mean and Covariance 846 11.8.2 State Prediction 846 11.8.3 State Filtering 848 11.9 Steady-State Kalman Filter 851 11.10 Linear Predictive Coding 857 11.11 Lattice Prediction-Error Filter 861 11.12 Levinson–Durbin Algorithm 865 11.13 Least-Squares Filtering 868 11.14 Recursive Least-Squares 872 Problems 876 Further Reading 879 12 Adaptive Filtering www.wiley.com/go/randomprocesses 880 12.1 Introduction 880 12.2 MSE Properties 880 12.3 Steepest Descent 889 12.4 Newton’s Method 894 12.5 LMS Algorithm 895 12.5.1 Convergence in the Mean 899 12.5.2 Convergence in the Mean-Square 901 12.5.3 Misadjustment 906 12.6 Modified LMS Algorithms 911 12.6.1 Sign-Error LMS Algorithm 911 12.6.2 Sign-Data LMS Algorithm 912 12.6.3 Sign-Sign LMS Algorithm 914 12.6.4 LMF Algorithm 914 12.6.5 Complex LMS Algorithm 916 12.6.6 “Leaky” LMS Algorithm 917 12.6.7 Normalized LMS Algorithm 918 12.6.8 Perceptron 920 12.6.9 Convergence of Modified LMS Algorithms 922 12.7 Adaptive IIR Filtering 923 12.7.1 Output-Error Formulation 924 12.7.2 Output-Error IIR Filter Algorithm 928 12.7.3 Equation-Error Formulation 932 12.7.4 Equation-Error Bias 933 Problems 936 Further Reading 939 13 Equalization, Beamforming, and Direction Finding www.wiley.com/go/randomprocesses 940 13.1 Introduction 940 13.2 Channel Equalization 941 13.3 Optimal Bussgang Algorithm 943 13.4 Blind Equalizer Algorithms 949 13.4.1 Sato’s Algorithm 949 13.4.2 Constant Modulus Algorithm 950 13.5 CMA Performance Surface 952 13.6 Antenna Arrays 958 13.7 Beampatterns 960 13.8 Optimal Beamforming 962 13.8.1 Known Look Direction 962 13.8.2 Multiple Constraint Beamforming 964 13.8.3 Training Signal 966 13.8.4 Maximum Likelihood 968 13.8.5 Maximum SNR and SINR 969 13.9 Adaptive Beamforming 970 13.9.1 LMS Beamforming 970 13.9.2 Constant Modulus Array 970 13.9.3 Decision-Directed Mode 973 13.9.4 Multistage CM Array 974 13.9.5 Output SINR and SNR 977 13.10 Direction Finding 981 13.10.1 Beamforming Approaches 981 13.10.2 MUSIC Algorithm 984 Problems 985 Further Reading 989

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Book SynopsisA one-of-a-kind resource on identifying and dealing with bias in statistical research on causal effects Do cell phones cause cancer? Can a new curriculum increase student achievement? Determining what the real causes of such problems are, and how powerful their effects may be, are central issues in research across various fields of study. Some researchers are highly skeptical of drawing causal conclusions except in tightly controlled randomized experiments, while others discount the threats posed by different sources of bias, even in less rigorous observational studies. Bias and Causation presents a complete treatment of the subject, organizing and clarifying the diverse types of biases into a conceptual framework. The book treats various sources of bias in comparative studiesboth randomized and observationaland offers guidance on how they should be addressed by researchers. Utilizing a relatively simple mathematical approach, the author develops a theory of bias thatTrade Review"The book combines a useful synthesis of the literature with an original working through of issues related to bias and causal inference. Anyone with a sustained interest in this topic will find the book worth reading." (Journal of Educational and Behavioral Statistics, May 2012) "...the book provides a unified framework for understanding issues of causal inference discussed differently across disciplines...the book will also be of substantial interest to methodologically minded readers working within specific disciplines but interested in methodological literature from other disciplines." (Journal of Educational and Behavioral Statistics, May 2012) "The book covers almost all the relevant biases that can be present when designing and analyzing treatment effects in comparative studies." (Journal of Biopharmaceutical Statistics, January 2011)"A consultant who specializes in applying statistics to various business and legal issues, Weisberg explains approaches to bias and causal inference, a realm statisticians have avoided until recently because it requires intuitive skills beyond the pale of mathematics. He writes for practicing researchers and methodologists and for students with a reasonably solid grounding in basic statistics and research methods." (SciTech Book News, December 2010)Table of ContentsPreface xi 1. What Is Bias? 1 1.1 Apples and Oranges, 2 1.2 Statistics vs. Causation, 3 1.3 Bias in the Real World, 6 Guidepost 1, 23 2. Causality and Comparative Studies 24 2.1 Bias and Causation, 24 2.2 Causality and Counterfactuals, 26 2.3 Why Counterfactuals? 32 2.4 Causal Effects, 33 2.5 Empirical Effects, 38 Guidepost 2, 46 3. Estimating Causal Effects 47 3.1 External Validity, 48 3.2 Measures of Empirical Effects, 50 3.3 Difference of Means, 52 3.4 Risk Difference and Risk Ratio, 55 3.5 Potential Outcomes, 57 3.6 Time-Dependent Outcomes, 60 3.7 Intermediate Variables, 63 3.8 Measurement of Exposure, 64 3.9 Measurement of the Outcome Value, 68 3.10 Confounding Bias, 70 Guidepost 3, 71 4. Varieties of Bias 72 4.1 Research Designs and Bias, 73 4.2 Bias in Biomedical Research, 81 4.3 Bias in Social Science Research, 85 4.4 Sources of Bias: A Proposed Taxonomy, 90 Guidepost 4, 92 5. Selection Bias 93 5.1 Selection Processes and Bias, 93 5.2 Traditional Selection Model: Dichotomous Outcome, 100 5.3 Causal Selection Model: Dichotomous Outcome, 102 5.4 Randomized Experiments, 104 5.5 Observational Cohort Studies, 108 5.6 Traditional Selection Model: Numerical Outcome, 111 5.7 Causal Selection Model: Numerical Outcome, 114 Guidepost 5, 121 Appendix, 122 6. Confounding: An Enigma? 126 6.1 What is the Real Problem? 127 6.2 Confounding and Extraneous Causes, 127 6.3 Confounding and Statistical Control, 131 6.4 Confounding and Comparability, 137 6.5 Confounding and the Assignment Mechanism, 139 6.6 Confounding and Model Specifi cation, 141 Guidepost 6, 144 7. Confounding: Essence, Correction, and Detection 145 7.1 Essence: The Nature of Confounding, 146 7.2 Correction: Statistical Control for Confounding, 172 7.3 Detection: Adequacy of Statistical Adjustment, 180 Guidepost 7, 191 Appendix, 192 8. Intermediate Causal Factors 195 8.1 Direct and Indirect Effects, 195 8.2 Principal Stratifi cation, 200 8.3 Noncompliance, 209 8.4 Attrition, 214 Guidepost 8, 215 9. Information Bias 217 9.1 Basic Concepts, 218 9.2 Classical Measurement Model: Dichotomous Outcome, 223 9.3 Causal Measurement Model: Dichotomous Outcome, 230 9.4 Classical Measurement Model: Numerical Outcome, 239 9.5 Causal Measurement Model: Numerical Outcome, 242 9.6 Covariates Measured with Error, 246 Guidepost 9, 250 10. Sources of Bias 252 10.1 Sampling, 254 10.2 Assignment, 260 10.3 Adherence, 266 10.4 Exposure Ascertainment, 269 10.5 Outcome Measurement, 273 Guidepost 10, 277 11. Contending with Bias 279 11.1 Conventional Solutions, 280 11.2 Standard Statistical Paradigm, 286 11.3 Toward a Broader Perspective, 288 11.4 Real-World Bias Revisited, 293 11.5 Statistics and Causation, 303 Glossary 309 Bibliography 321 Index 340

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Book SynopsisAn introductory guide to smoothing techniques, semiparametric estimators, and their related methods, this book describes the methodology via a selection of carefully explained examples and data sets. It also demonstrates the potential of these techniques using detailed empirical examples drawn from the social and political sciences.Trade Review"The strength of Keele's book is that it offers clear, straightforward explanations of the models, illustrated with social science (primarily political science) applications. Applied social science researchers should be able to incorporate these methods in their own research relatively easily after reading this book." (The Political Methodologist, 2009)Table of ContentsList of Tables. List of Figures. Preface. 1 Introduction: Global versus Local Statistics. 1.1 The Consequences of Ignoring Nonlinearity. 1.2 Power Transformations. 1.3 Nonparametric and Semiparametric Techniques. 1.4 Outline of the Text. 2 Smoothing and Local Regression. 2.1 Simple Smoothing. 2.1.1 Local Averaging. 2.1.2 Kernel Smoothing. 2.2 Local Polynomial Regression. 2.3 Nonparametric Modeling Choices. 2.3.1 The Span. 2.3.2 Polynomial Degree and Weight Function. 2.3.3 A Note on Interpretation. 2.4 Statistical Inference for Local Polynomial Regression. 2.5 Multiple Nonparametric Regression. 2.6 Conclusion. 2.7 Exercises. 3 Splines. 3.1 Simple Regression Splines. 3.1.1 Basis Functions. 3.2 Other Spline Models and Bases. 3.2.1 Quadratic and Cubic Spline Bases. 3.2.2 Natural Splines. 3.2.3 B-splines. 3.2.4 Knot Placement and Numbers. 3.2.5 Comparing Spline Models. 3.3 Splines and Overfitting. 3.3.1 Smoothing Splines. 3.3.2 Splines as Mixed Models. 3.3.3 Final Notes on Smoothing Splines. 3.3.4 Thin Plate Splines. 3.4 Inference for Splines. 3.5 Comparisons and Conclusions. 3.6 Exercises. 4 Automated Smoothing Techniques. 4.1 Span by Cross-Validation. 4.2 Splines and Automated Smoothing. 4.2.1 Estimating Smoothing Through the Likelihood. 4.2.2 Smoothing Splines and Cross-Validation. 4.3 Automated Smoothing in Practice. 4.4 Automated Smoothing Caveats. 4.5 Exercises. 5 Additive and Semiparametric Regression Models. 5.1 Additive Models. 5.2 Semiparametric Regression Models. 5.3 Estimation. 5.3.1 Backfitting. 5.4 Inference. 5.5 Examples. 5.5.1 Congressional Elections. 5.5.2 Feminist Attitudes. 5.6 Discussion. 5.7 Exercises. 6 Generalized Additive Models. 6.1 Generalized Linear Models. 6.2 Estimation of GAMS. 6.3 Statistical Inference. 6.4 Examples. 6.4.1 Logistic Regression: The Liberal Peace. 6.4.2 Ordered Logit: Domestic Violence. 6.4.3 Count Models: Supreme Court Overrides. 6.4.4 Survival Models: Race Riots. 6.5 Discussion. 6.6 Exercises. 7 Extensions of the Semiparametric Regression Model. 7.1 Mixed Models. 7.2 Bayesian Smoothing. 7.3 Propensity Score Matching. 7.4 Conclusion. 8 Bootstrapping. 8.1 Classical Inference. 8.2 Bootstrapping – An Overview. 8.2.1 Bootstrapping. 8.2.2 An Example: Bootstrapping the Mean. 8.2.3 Bootstrapping Regression Models. 8.2.4 An Example: Presidential Elections. 8.3 Bootstrapping Nonparametric and Semiparametric Regression Models. 8.3.1 Bootstrapping Nonparametric Fits. 8.3.2 Bootstrapping Nonlinearity Tests. 8.4 Conclusion. 8.5 Exercises. 9 Epilogue. Appendix: Software. Bibliography. Author Index. Subject Index.

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Book SynopsisThis book offers an innovative introduction to social research. The book explores all stages of the research process and it features both quantitative and qualitative methods. Research design topics include sampling techniques, choosing a research design, and determining research question that inform public opinion and direct future studies. Throughout the book, the authors provide vivid and engaging examples that reinforce the reading and understanding of social science research. Your Turn boxes contain activities that allow students to practice research skills, such as sampling, naturalistic observation, survey collection, coding, analysis, and report writing.Table of ContentsAbout the Authors. Preface. Introduction. CHAPTER 1: UNDERSTANDING RESEARCH. The Research Process. Types of Research. Research Proposals. Research Ethics. Getting Acquainted with SPSS. Summary. Key Terms. CHAPTER 2: THE WHO, HOW, AND WHY OF RESEARCH. Who: Selecting a Sample. How: Selecting a Research Strategy. Why: Doing Research That Makes a Difference. Summary. Key Terms. CHAPTER 3: QUANTITATIVE RESEARCH: MEASUREMENT AND DATA COLLECTION. Measurement: Turning Abstractions into Variables. Characteristics of Good Measures. Collecting Data. Summary. Key Terms. CHAPTER 4: QUANTITATIVE RESEARCH: DESCRIPTIVE AND CORRELATIONAL DESIGNS. Basic Concepts. Causation and Prediction. Data Gathering. Data Analysis. Summary. Key Terms. CHAPTER 5: QUANTITATIVE RESEARCH: BASIC EXPERIMENTAL DESIGNS. Experimental Validity. Types of Variables. Characteristics of Experiments. Types of Experimental Designs. Data Analysis. Summary. Key Terms. CHAPTER 6: QUANTITATIVE RESEARCH: ADVANCED EXPERIMENTAL DESIGNS. Basic Concepts. Repeated-Measures Designs. Complex Designs. Quasi-Experimental Designs. Data Analysis. Summary. Key Terms. CHAPTER 7: WHAT IS QUALITATIVE RESEARCH? Telling a Story . . . Qualitatively. Two Worldviews on Research: Reality and Knowledge. Comparison of Quantitative and Qualitative Research. Critique of Quantitative Research. Crisis of Representation. Summary. Key Terms. CHAPTER 8: PLANNING YOUR QUALITATIVE STUDY: DESIGN, SAMPLING, AND DATA ANALYSIS. Designing Qualitative Research. Summary. Key Terms. CHAPTER 9: QUALITATIVE RESEARCH METHODS: ETHNOGRAPHY, PHENOMENOLOGY, CASE STUDY, TEXTUAL ANALYSIS, AND APPLIED RESEARCH. Ethnography. Phenomenology. Case Study. Textual Analysis. Applied Research Methods: Action and Evaluation Research. Summary. Key Terms. CHAPTER 10: QUALITATIVE RESEARCH TOOLS: INTERVIEWING, FOCUS GROUPS, AND OBSERVATION. The First Tool: Defi ning the Context. Qualitative Research Tools: How to Collect Data. Summary. Key Terms. CHAPTER 11: PRESENTING YOUR RESEARCH FINDINGS. Presenting Your Research with a Poster. Presenting Your Research in an Oral Presentation. Presenting Your Research in a Paper. Reducing Bias in Research Reporting. Summary. Key Terms. References. Appendix A: A Sample Manuscript from a Quantitative Study. Appendix B: A Sample Manuscript from a Qualitative Study. Glossary. Index.

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Book SynopsisThis book is an accessible introduction to quantitative data analysis, concentrating on the key issues facing those new to research, such as how to decide which statistical procedure is suitable, and how to interpret the subsequent results.Table of ContentsTables, Figures, Exhibits, and Boxes xi Preface xxiii The Author xxvii Introduction xxix 1 CROSS-TABULATIONS 1 What This Chapter Is About 1 Introduction to the Book via a Concrete Example 2 Cross-Tabulations 8 What This Chapter Has Shown 19 2 MORE ON TABLES 21 What This Chapter Is About 21 The Logic of Elaboration 22 Suppressor Variables 25 Additive and Interaction Effects 26 Direct Standardization 28 A Final Note on Statistical Controls Versus Experiments 43 What This Chapter Has Shown 45 3 STILL MORE ON TABLES 47 What This Chapter Is About 47 Reorganizing Tables to Extract New Information 48 When to Percentage a Table "Backwards" 50 Cross-Tabulations in Which the Dependent Variable Is Represented by a Mean 52 Index of Dissimilarity 58 Writing About Cross-Tabulations 61 What This Chapter Has Shown 63 4 ON THE MANIPULATION OF DATA BY COMPUTER 65 What This Chapter Is About 65 Introduction 66 How Data Files Are Organized 67 Transforming Data 72 What This Chapter Has Shown 80 Appendix 4.A Doing Analysis Using Stata 80 Tips on Doing Analysis Using Stata 80 Some Particularly Useful Stata 10.0 Commands 84 5 INTRODUCTION TO CORRELATION AND REGRESSION (ORDINARY LEAST SQUARES) 87 What This Chapter Is About 87 Introduction 88 Quantifying the Size of a Relationship: Regression Analysis 89 Assessing the Strength of a Relationship: Correlation Analysis 91 The Relationship Between Correlation and Regression Coeffi cients 94 Factors Affecting the Size of Correlation (and Regression) Coeffi cients 94 Correlation Ratios 99 What This Chapter Has Shown 102 6 INTRODUCTION TO MULTIPLE CORRELATION AND REGRESSION (ORDINARY LEAST SQUARES) 103 What This Chapter Is About 103 Introduction 104 A Worked Example: The Determinants of Literacy in China 113 Dummy Variables 120 A Strategy for Comparisons Across Groups 124 A Bayesian Alternative for Comparing Models 133 Independent Validation 135 What This Chapter Has Shown 136 7 MULTIPLE REGRESSION TRICKS: TECHNIQUES FOR HANDLING SPECIAL ANALYTIC PROBLEMS 139 What This Chapter Is About 139 Nonlinear Transformations 140 Testing the Equality of Coeffi cients 147 Trend Analysis: Testing the Assumption of Linearity 149 Linear Splines 152 Expressing Coeffi cients as Deviations from the Grand Mean (Multiple Classifi cation Analysis) 164 Other Ways of Representing Dummy Variables 166 Decomposing the Difference Between Two Means 172 What This Chapter Has Shown 179 8 MULTIPLE IMPUTATION OF MISSING DATA 181 What This Chapter Is About 181 Introduction 182 A Worked Example: The Effect of Cultural Capital on Educational Attainment in Russia 187 What This Chapter Has Shown 194 9 SAMPLE DESIGN AND SURVEY ESTIMATION 195 What This Chapter Is About 195 Survey Samples 196 Conclusion 223 What This Chapter Has Shown 224 10 REGRESSION DIAGNOSTICS 225 What This Chapter Is About 225 Introduction 226 A Worked Example: Societal Differences in Status Attainment 229 Robust Regression 237 Bootstrapping and Standard Errors 238 What This Chapter Has Shown 240 11 SCALE CONSTRUCTION 241 What This Chapter Is About 241 Introduction 242 Validity 242 Reliability 243 Scale Construction 246 Errors-in-Variables Regression 258 What This Chapter Has Shown 261 12 LOG-LINEAR ANALYSIS 263 What This Chapter Is About 263 Introduction 264 Choosing a Preferred Model 265 Parsimonious Models 277 A Bibliographic Note 294 What This Chapter Has Shown 295 Appendix 12.A Derivation of the Effect Parameters 295 Appendix 12.B Introduction to Maximum Likelihood Estimation 297 Mean of a Normal Distribution 298 Log-Linear Parameters 299 13 BINOMIAL LOGISTIC REGRESSION 301 What This Chapter Is About 301 Introduction 302 Relation to Log-Linear Analysis 303 A Worked Logistic Regression Example: Predicting Prevalence of Armed Threats 304 A Second Worked Example: Schooling Progression Ratios in Japan 314 A Third Worked Example (Discrete-Time Hazard-Rate Models): Age at First Marriage 318 A Fourth Worked Example (Case-Control Models): Who Was Appointed to a Nomenklatura Position in Russia? 327 What This Chapter Has Shown 329 Appendix 13.A Some Algebra for Logs and Exponents 330 Appendix 13.B Introduction to Probit Analysis 330 14 MULTINOMIAL AND ORDINAL LOGISTIC REGRESSION AND TOBIT REGRESSION 335 What This Chapter Is About 335 Multinomial Logit Analysis 336 Ordinal Logistic Regression 342 Tobit Regression (and Allied Procedures) for Censored Dependent Variables 353 Other Models for the Analysis of Limited Dependent Variables 360 What This Chapter Has Shown 361 15 IMPROVING CAUSAL INFERENCE: FIXED EFFECTS AND RANDOM EFFECTS MODELING 363 What This Chapter Is About 363 Introduction 364 Fixed Effects Models for Continuous Variables 365 Random Effects Models for Continuous Variables 371 A Worked Example: The Determinants of Income in China 372 Fixed Effects Models for Binary Outcomes 375 A Bibliographic Note 380 What This Chapter Has Shown 380 16 FINAL THOUGHTS AND FUTURE DIRECTIONS: RESEARCH DESIGN AND INTERPRETATION ISSUES 381 What this Chapter is About 381 Research Design Issues 382 The Importance of Probability Sampling 397 A Final Note: Good Professional Practice 400 What This Chapter Has Shown 405 Appendix A: Data Descriptions and Download Locations for the Data Used in This Book 407 Appendix B: Survey Estimation with the General Social Survey 411 References 417 Index 431

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Book SynopsisA comprehensive look at how probability and statistics is applied to the investment process Finance has become increasingly more quantitative, drawing on techniques in probability and statistics that many finance practitioners have not had exposure to before.Table of ContentsPreface xv About the Authors xvii Chapter 1 Introduction 1 Probability vs. Statistics 4 Overview of the Book 5 Part One Descriptive Statistics 15 Chapter 2 Basic Data Analysis 17 Data Types 17 Frequency Distributions 22 Empirical Cumulative Frequency Distribution 27 Data Classes 32 Cumulative Frequency Distributions 41 Concepts Explained in this Chapter 43 Chapter 3 Measures of Location and Spread 45 Parameters vs. Statistics 45 Center and Location 46 Variation 59 Measures of the Linear Transformation 69 Summary of Measures 71 Concepts Explained in this Chapter 73 Chapter 4 Graphical Representation of Data 75 Pie Charts 75 Bar Chart 78 Stem and Leaf Diagram 81 Frequency Histogram 82 Ogive Diagrams 89 Box Plot 91 QQ Plot 96 Concepts Explained in this Chapter 99 Chapter 5 Multivariate Variables and Distributions 101 Data Tables and Frequencies 101 Class Data and Histograms 106 Marginal Distributions 107 Graphical Representation 110 Conditional Distribution 113 Conditional Parameters and Statistics 114 Independence 117 Covariance 120 Correlation 123 Contingency Coefficient 124 Concepts Explained in this Chapter 126 Chapter 6 Introduction to Regression Analysis 129 The Role of Correlation 129 Regression Model: Linear Functional Relationship Between Two Variables 131 Distributional Assumptions of the Regression Model 133 Estimating the Regression Model 134 Goodness of Fit of the Model 138 Linear Regression of Some Nonlinear Relationship 140 Two Applications in Finance 142 Concepts Explained in this Chapter 149 Chapter 7 Introduction to Time Series Analysis 153 What Is Time Series? 153 Decomposition of Time Series 154 Representation of Time Series with Difference Equations 159 Application: The Price Process 159 Concepts Explained in this Chapter 163 Part Two Basic Probability Theory 165 Chapter 8 Concepts of Probability Theory 167 Historical Development of Alternative Approaches to Probability 167 Set Operations and Preliminaries 170 Probability Measure 177 Random Variable 179 Concepts Explained in this Chapter 185 Chapter 9 Discrete Probability Distributions 187 Discrete Law 187 Bernoulli Distribution 192 Binomial Distribution 195 Hypergeometric Distribution 204 Multinomial Distribution 211 Poisson Distribution 216 Discrete Uniform Distribution 219 Concepts Explained in this Chapter 221 Chapter 10 Continuous Probability Distributions 229 Continuous Probability Distribution Described 229 Distribution Function 230 Density Function 232 Continuous Random Variable 237 Computing Probabilities from the Density Function 238 Location Parameters 239 Dispersion Parameters 239 Concepts Explained in this Chapter 245 Chapter 11 Continuous Probability Distributions with Appealing Statistical Properties 247 Normal Distribution 247 Chi-Square Distribution 254 Student’s t-Distribution 256 F-Distribution 260 Exponential Distribution 262 Rectangular Distribution 266 Gamma Distribution 268 Beta Distribution 269 Log-Normal Distribution 271 Concepts Explained in this Chapter 275 Chapter 12 Continuous Probability Distributions Dealing with Extreme Events 277 Generalized Extreme Value Distribution 277 Generalized Pareto Distribution 281 Normal Inverse Gaussian Distribution 283 α-Stable Distribution 285 Concepts Explained in this Chapter 292 Chapter 13 Parameters of Location and Scale of Random Variables 295 Parameters of Location 296 Parameters of Scale 306 Concepts Explained in this Chapter 321 Appendix: Parameters for Various Distribution Functions 322 Chapter 14 Joint Probability Distributions 325 Higher Dimensional Random Variables 326 Joint Probability Distribution 328 Marginal Distributions 333 Dependence 338 Covariance and Correlation 341 Selection of Multivariate Distributions 347 Concepts Explained in this Chapter 358 Chapter 15 Conditional Probability and Bayes’ Rule 361 Conditional Probability 362 Independent Events 365 Multiplicative Rule of Probability 367 Bayes’ Rule 372 Conditional Parameters 374 Concepts Explained in this Chapter 377 Chapter 16 Copula and Dependence Measures 379 Copula 380 Alternative Dependence Measures 406 Concepts Explained in this Chapter 412 Part Three Inductive Statistics 413 Chapter 17 Point Estimators 415 Sample, Statistic, and Estimator 415 Quality Criteria of Estimators 428 Large Sample Criteria 435 Maximum Likehood Estimator 446 Exponential Family and Sufficiency 457 Concepts Explained in this Chapter 461 Chapter 18 Confidence Intervals 463 Confidence Level and Confidence Interval 463 Confidence Interval for the Mean of a Normal Random Variable 466 Confidence Interval for the Mean of a Normal Random Variable with Unknown Variance 469 Confidence Interval for the Variance of a Normal Random Variable 471 Confidence Interval for the Variance of a Normal Random Variable with Unknown Mean 474 Confidence Interval for the Parameter p of a Binomial Distribution 475 Confidence Interval for the Parameter λ of an Exponential Distribution 477 Concepts Explained in this Chapter 479 Chapter 19 Hypothesis Testing 481 Hypotheses 482 Error Types 485 Quality Criteria of a Test 490 Examples 496 Concepts Explained in this Chapter 518 Part Four Multivariate Linear Regression Analysis 519 Chapter 20 Estimates and Diagnostics for Multivariate Linear Regression Analysis 521 The Multivariate Linear Regression Model 522 Assumptions of the Multivariate Linear Regression Model 523 Estimation of the Model Parameters 523 Designing the Model 526 Diagnostic Check and Model Significance 526 Applications to Finance 531 Concepts Explained in this Chapter 543 Chapter 21 Designing and Building a Multivariate Linear Regression Model 545 The Problem of Multicollinearity 545 Incorporating Dummy Variables as Independent Variables 548 Model Building Techniques 561 Concepts Explained in this Chapter 565 Chapter 22 Testing the Assumptions of the Multivariate Linear Regression Model 567 Tests for Linearity 568 Assumed Statistical Properties about the Error Term 570 Tests for the Residuals Being Normally Distributed 570 Tests for Constant Variance of the Error Term (Homoskedasticity) 573 Absence of Autocorrelation of the Residuals 576 Concepts Explained in this Chapter 581 Appendix A Important Functions and Their Features 583 Continuous Function 583 Indicator Function 586 Derivatives 587 Monotonic Function 591 Integral 592 Some Functions 596 Appendix B Fundamentals of Matrix Operations and Concepts 601 The Notion of Vector and Matrix 601 Matrix Multiplication 602 Particular Matrices 603 Positive Semidefinite Matrices 614 Appendix C Binomial and Multinomial Coefficients 615 Binomial Coefficient 615 Multinomial Coefficient 622 Appendix D Application of the Log-Normal Distribution to the Pricing of Call Options 625 Call Options 625 Deriving the Price of a European Call Option 626 Illustration 631 References 633 Index 635

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Book SynopsisA new edition of the classic guide to the use of statistics in medicine, featuring examples from articles in the New England Journal of Medicine Medical Uses of Statistics has served as one of the most influential works on the subject for physicians, physicians-in-training, and a myriad of healthcare experts who need a clear idea of the proper application of statistical techniques in clinical studies as well as the implications of their interpretation for clinical practice. This Third Edition maintains the focus on the critical ideas, rather than the mechanics, to give practitioners and students the resources they need to understand the statistical methods they encounter in modern medical literature. Bringing together contributions from more than two dozen distinguished statisticians and medical doctors, this volume stresses the underlying concepts in areas such as randomized trials, survival analysis, genetics, linear regression, meta-analyTrade Review"Medical Uses of Statistics, 3rd Edition" presents the concepts of medical statistics across a broad range of topics with a practical perspective, a moderate level of detail, and a minimal number of formulae... The text is clearly written in a consistent style." (Journal of Clinical Research Best Practices, November 2010) Table of ContentsContributors. Preface. Preface to the Second Edition. Preface to the First Edition. Acknowledgments. Origins of Chapters. Introduction. SECTION I: BROAD CONCEPTS AND ANALYTIC TECHNIQUES. Chapter 1 Statistical Concepts Fundamental to Investigations (Lincoln E. Moses). Chapter 2 Some Uses of Statistical Thinking (John C. Bailar III). Chapter 3 Use of Statistical Analysis in the New England Journal of Medicine (Shilpi Agarwal, Graham A. Colditz, and John D. Emerson). SECTION II: DESIGN. Chapter 4 Randomized Trials and Other Parallel Comparisons of Treatment (Nancy E. Mayo). Chapter 5 Crossover and Self-Controlled Designs in Clinical Research (John C. Bailar III, Thomas A. Louis, Philip W. Lavori, and Marcia Polansky). Chapter 6 The Series of Consecutive Cases as a Device for Assessing Outcomes of Interventions (Lincoln E. Moses). Chapter 7 Biostatistics in Epidemiology: Design and Basic Analysis (Mark S. Goldberg). SECTION III: ANALYSIS. Chapter 8 p-Values (James H. Ware, Frederick Mosteller, Fernando Delgado, Christl Donnelly, and Joseph A. Ingelfinger). Chapter 9 Understanding Analyses of Randomized Trials (Nancy E. Mayo). Chapter 10 Linear Regression in Medical Research (Paul J. Rathouz and Amita Rastogi). Chapter 11 Statistical Analysis of Survival Data (Stephen W. Lagakos). Chapter 12 Analysis of Categorical Data in Medical Studies (Paul S. Albert). Chapter 13 Analyzing Data from Ordered Categories (Lincoln E. Moses, John D. Emerson, and Hossein Hosseini). SECTION IV: COMMUNICATING RESULTS. Chapter 14 Guidelines for Statistical Reporting in Articles for Medical Journals: Amplifications and Explanations (John C. Bailar III and Frederick Mosteller). Chapter 15 Reporting of Subgroup Analyses in Clinical Trials (Rui Wang, Stephen W. Lagakos, James H. Ware, David J. Hunter, and Jeffrey M. Drazen). Chapter 16 Writing about Numbers (Frederick Mosteller, Margaret Perkins, and Stephen Morrissey). SECTION V: SPECIALIZED METHODS. Chapter 17 Combining Results from Independent Studies: Systematic Reviews and Meta-Analysis in Clinical Research (Michael A. Stoto). Chapter 18 Biostatistics in Epidemiology: Advanced Methods of Regression Analysis (Mark S. Goldberg). Chapter 19 Genetic Inference (Dan L. Nicolae, Thorsten Kurz, and Carole Ober). Chapter 20 Identifying Disease Genes in Association Studies (Dan L. Nicolae, Thorsten Kurz, and Carole Ober). Chapter 21 Risk Assessment (A. John Bailer and John C. Bailar III). INDEX.

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Book SynopsisPraise for the First Edition . . . an excellent addition to an upper-level undergraduate course on environmental statistics, and . . . a ''must-have'' desk reference for environmental practitioners dealing with censored datasets. ?Vadose Zone Journal Statistics for Censored Environmental Data Using Minitab and R, Second Edition introduces and explains methods for analyzing and interpreting censored data in the environmental sciences. Adapting survival analysis techniques from other fields, the book translates well-established methods from other disciplines into new solutions for environmental studies. This new edition applies methods of survival analysis, including methods for interval-censored data to the interpretation of low-level contaminants in environmental sciences and occupational health. Now incorporating the freely available R software as well as Minitab into the discussed analyses, the book features neTrade Review“Helsel’s book is an excellent resource for scientists and statisticians, as well as an effective textbook for advanced undergraduate and graduate school students.” (Integrated Environmental Assessment and Management, 1 May 2014)Table of ContentsPreface ix Acknowledgments xi Introduction to the First Edition: An Accident Waiting to Happen xiii Introduction to the Second Edition: Invasive Data xvii 1 Things People Do with Censored Data that Are Just Wrong 1 Why Not Substitute—Missing the Signals that Are Present in the Data 3 Why Not Substitute?—Finding Signals that Are Not There 8 So Why Not Substitute? 10 Other Common Misuses of Censored Data 10 2 Three Approaches for Censored Data 12 Approach 1: Nonparametric Methods after Censoring at the Highest Reporting Limit 13 Approach 2: Maximum Likelihood Estimation 14 Approach 3: Nonparametric Survival Analysis Methods 17 Application of Survival Analysis Methods to Environmental Data 17 Parallels to Uncensored Methods 21 3 Reporting Limits 22 Limits When the Standard Deviation is Considered Constant 23 Insider Censoring–Biasing Interpretations 29 Reporting the Machine Readings of all Measurements 33 Limits When the Standard Deviation Changes with Concentration 34 For Further Study 36 4 Reporting, Storing, and Using Censored Data 37 Reporting and Storing Censored Data 37 Using Interval-Censored Data 41 Exercises 42 5 Plotting Censored Data 44 Boxplots 44 Histograms 46 Empirical Distribution Function 47 Survival Function Plots 49 Probability Plot 52 X–Y Scatterplots 59 Exercises 61 6 Computing Summary Statistics and Totals 62 Nonparametric Methods after Censoring at the Highest Reporting Limit 62 Maximum Likelihood Estimation 64 The Nonparametric Kaplan–Meier and Turnbull Methods 70 ROS: A “Robust” Imputation Method 79 Methods in Excel 86 Handling Data with High Reporting Limits 86 A Review of Comparison Studies 87 Summing Data with Censored Observations 94 Exercises 98 7 Computing Interval Estimates 99 Parametric Intervals 100 Nonparametric Intervals 103 Intervals for Censored Data by Substitution 103 Intervals for Censored Data by Maximum Likelihood 104 Intervals for the Lognormal Distribution 112 Intervals Using “Robust” Parametric Methods 125 Nonparametric Intervals for Censored Data 126 Bootstrapped Intervals 136 For Further Study 140 Exercises 141 8 What Can be Done When All Data Are Below the Reporting Limit? 142 Point Estimates 143 Probability of Exceeding the Reporting Limit 144 Exceedance Probability for a Standard Higher than the Reporting Limit 148 Hypothesis Tests Between Groups 151 Summary 152 Exercises 152 9 Comparing Two Groups 153 Why Not Use Substitution? 154 Simple Nonparametric Methods After Censoring at the Highest Reporting Limit 156 Maximum Likelihood Estimation 161 Nonparametric Methods 167 Value of the Information in Censored Observations 178 Interval-Censored Score Tests: Testing Data that Include (DL to RL) Values 180 Paired Observations 183 Summary of Two-Sample Tests for Censored Data 192 Exercises 192 10 Comparing Three or More Groups 194 Substitution Does Not Work—Invasive Data 195 Nonparametric Methods after Censoring at the Highest Reporting Limit 196 Maximum Likelihood Estimation 199 Nonparametric Method—The Generalized Wilcoxon Test 209 Summary 215 Exercises 216 11 Correlation 218 Types of Correlation Coefficients 218 Nonparametric Methods after Censoring at the Highest Reporting Limit 219 Maximum Likelihood Correlation Coefficient 224 Nonparametric Correlation Coefficient—Kendall’s Tau 227 Interval-Censored Score Tests: Testing Correlation with (DL to RL) Values 230 Summary: A Comparison Among Methods 232 For Further Study 234 Exercises 235 12 Regression and Trends 236 Why Not Substitute? 237 Nonparametric Methods After Censoring at the Highest Reporting Limit 239 Maximum Likelihood Estimation 249 Akritas–Theil–Sen Nonparametric Regression 258 Additional Methods for Censored Regression 264 Exercises 266 13 Multivariate Methods for Censored Data 268 A Brief Overview of Multivariate Procedures 269 Nonparametric Methods After Censoring at the Highest Reporting Limit 273 Multivariate Methods for Data with Multiple Reporting Limits 288 Summary of Multivariate Methods for Censored Data 296 14 The NADA for R Software 297 A Brief Overview of R and the NADA Software 297 Summary of the Commands Available in NADA 300 Appendix: Datasets 303 References 309 Index 321

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Book SynopsisPresenting a concise, well-rounded focus on the statistical concepts and applications that are essential for understanding gathered data in the earth and atmospheric sciences.Table of ContentsPreface v Contributors 1 1 Adaptive Sampling 1 2 Agricultural Surveys 8 3 Allometry 20 4 Atmospheric Statistics 27 5 Capture—Recapture Methods—I 35 6 Capture-Recapture Methods—II 43 7 Cluster Sampling 50 8 Distance Sampling 53 9 Ecological Statistics 59 10 Environmental Statistics 67 11 Estimation of Species Richness and Shared Species Richness 76 12 Geographic Information Systems 112 13 Geostatistics 121 14 Landsat Data Analysis in Crop Area Estimation 130 15 Latin Hypercube Sampling 140 16 Line Intercept Sampling 146 17 Line Transect Sampling 148 18 Methods for Drought Analysis and Forecasting 150 19 Ranked Set Sampling Methodology for Environmental Data 185 20 Spatial Data Analysis 212 21 Spatial Processes 216 22 Spatial Sampling 223 23 Statistics in Agriculture 228 24 Statistics in Animal Science 232 25 Statistics in Biogeography 239 26 Statistics in Fisheries Research 246 27 Statistics in Forestry 251 28 Statistics in Geography 266 29 Statistics in Geology 272 30 Statistics in Geophysics 276 31 Statistics in Ornithology 292 32 Stereology 304 33 Stylometry 310 34 Systematic Sampling 318 35 Traffic Flow Problems 322 36 Transect Methods 326 37 Weather Modification—I 331 38 Weather Modification—II 338 39 Wildlife Sampling 349 Index 354

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Book SynopsisPraise for the First Edition . . . an excellent textbook . . . an indispensable reference for biostatisticians and epidemiologists. International Statistical Institute A new edition of the definitive guide to classical and modern methods of biostatistics Biostatistics consists of various quantitative techniques that are essential to the description and evaluation of relationships among biologic and medical phenomena. Biostatistical Methods: The Assessment of Relative Risks, Second Edition develops basic concepts and derives an expanded array of biostatistical methods through the application of both classical statistical tools and more modern likelihood-based theories. With its fluid and balanced presentation, the book guides readers through the important statistical methods for the assessment of absolute and relative risks in epidemiologic studies and clinical trials with categorical, count, and event-time data. Presenting a brTrade Review"Biostatistical methods, second edition is an excellent book for biostatistics courses at the graduate level. It is also an invaluable reference for biostatisticians, applied statisticians, and epidemiologists." (Mathematical Reviews, 2011) "The author of this book has made a tremendous effort in covering a gamut of tests, methods, and ideas for biostatistical problem solving . . . In conclusion, the book is recommended to all in biostatistics as a technical reference." (Journal of Biopharmaceutical Statistics, 1 September 2012) "...Biostatistics is set apart from other statistics specialties by its focus on the assessment of risks and relative risks through clinical research," states Lachin (George Washington U.) in the preface to the first edition (2001). He developed this graduate text to support a course he launched as a joint initiative of the university's department of statistics, its Biostatistics Center, and the School of Public Health and Health Services. Coverage includes discussion of biostatistics and biomedical science, relative risk estimates and tests for independent groups, sample size, stratified adjusted analysis, case-control and matched studies, applications of maximum likelihood and efficient scores, among other topics." (Book News Inc., February 2011) Table of ContentsPreface. Preface to First Edition. 1 Biostatistics and Biomedical Science. 1.1 Statistics and the Scientific Method. 1.2 Biostatistics. 1.3 Natural History of Disease Progression. 1.4 Types of Biomedical Studies. 1.5 Studies of Diabetic Nephropathy. 2 Relative Risk Estimates and Tests for Independent Groups. 2.1 Probability As a Measure of Risk. 2.2 Measures of Relative Risk. 2.3 Large Sample Distribution. 2.4 Sampling Models Likelihoods. 2.5 Exact Inference. 2.6 Large Sample Inferences. 2.7 SAS PROC FREQ. 2.8 Other Measures of Differential Risk. 2.9 Polychotomous and Ordinal Data. 2.10 Two Independent Groups With Polychotomous Response. 2.11 Multiple Independent Groups. 2.12 Problems. 3 Sample Size, Power, and Efficiency. 3.1 Estimation Precision. 3.2 Power of Z-Tests. 3.3 Test for Two Proportions. 3.4 Power of Chi-Square Tests. 3.5 SAS PROC POWER. 3.6 Efficiency. 3.7 Problems. 4 Stratified-Adjusted Analysis for Independent Groups. 4.1 Introduction. 4.2 Mantel-Haenszel Test and Cochran’s Test. 4.3 Stratified-Adjusted Estimators. 4.4 Nature of Covariate Adjustment. 4.5 Multivariate Tests of Hypotheses. 4.6 Tests of Homogeneity. 4.7 Efficient Tests of No Partial Association. 4.8 Asymptotic Relative Efficiency of Competing Tests. 4.9 Maximin-Efficient Robust Tests. 4.10 Random Effects Model. 4.11 Power and Sample Size for Tests of Association. 4.12 Polychotomous and Ordinal Data. 4.13 Problems. 5 Case-Control and Matched Studies. 5.1 Unmatched Case-Control (Retrospective) Sampling. 5.2 Matching. 5.3 Tests of Association for Matched Pairs. 5.4 Measures of Association for Matched Pairs. 5.5 Pair-Matched Retrospective Study. 5.6 Power Function of McNemar’s Test. 5.7 Stratified Analysis of Pair-Matched Tables. 5.8 Multiple Matching-Mantel-Haenszel Analysis. 5.9 Matched Polychotomous Data. 5.10 Kappa Index of Agreement. 5.11 Problems. 6 Applications of Maximum Likelihood and Efficient Scores. 6.1 Binomial. 6.2 2x2 Table: Product Binomial (Unconditionally). 6.3 2x2 Table, Conditionally. 6.4 Score-Based Estimate. 6.5 Stratified Score Analysis of Independent 2x2 Tables. 6.6 Matched Pairs. 6.7 Iterative Maximum Likelihood. 6.8 Problems. 7 Logistic Regression Models. 7.1 Unconditional Logistic Regression Model. 7.2 Interpretation of the Logistic Regression Model. 7.3 Tests of Significance. 7.4 Interactions. 7.5 Measures of the Strength of Association. 7.6 Conditional Logistic Regression Model for Matched Sets. 7.7 Models for Polychotomous or Ordinal Data. 7.8 Random Effects and Mixed Models. 7.9 Models for Multivariate or Repeated Measures. 7.10 Problems. 8 Analysis of Count Data. 8.1 Event Rates and the Homogeneous Poisson Model. 8.2 Over Dispersed Poisson Model. 8.3 Poisson Regression Model. 8.4 Over Dispersed and Robust Poisson Regression. 8.5 Conditional Poisson Regression for Matched Sets. 8.6 Negative Binomial Models. 8.7 Power and Sample Size. 8.8 Multiple Outcomes. 8.9 Problems. 9 Analysis of Event-Time Data. 9.1 Introduction to Survival Analysis. 9.2 Lifetable Construction. 9.3 Family of Weighted Mantel-Haenszel Tests. 9.4 Proportional Hazards Models. 9.5 Evaluation of Sample Size and Power. 9.6 Additional Models. 9.7 Analysis of Recurrent Events. 9.8 Problems. Appendix Statistical Theory. A.1 Introduction. A.2 Central Limit Theorem and the Law of Large Numbers. A.3 Delta Method. A.4 Slutsky’s Convergence Theorem. A.5 Least Squares Estimation. A.6 Maximum Likelihood Estimation and Efficient Scores. A.7 Tests of Significance. A.8 Explained Variation. A.9 Robust Inference. A.10 Generalized Linear Models and Quasi-Likelihood. A.11 Generalized Estimating Equations (GEE). References. Author Index. Subject Index.

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Book SynopsisA vivid, hands-on discussion of the statistical methods in imaging, optics, and photonics applications In the field of imaging science, there is a growing need for students and practitioners to be equipped with the necessary knowledge and tools to carry out quantitative analysis of data. Providing a self-contained approach that is not too heavily statistical in nature, Statistics for Imaging, Optics, and Photonics presents necessary analytical techniques in the context of real examples from various areas within the field, including remote sensing, color science, printing, and astronomy. Bridging the gap between imaging, optics, photonics, and statistical data analysis, the author uniquely concentrates on statistical inference, providing a wide range of relevant methods. Brief introductions to key probabilistic terms are provided at the beginning of the book in order to present the notation used, followed by discussions on multivariate techniques such as: Trade Review“In a word, this is a well-structured volume which will meet the demand visualised by the author.” (Contemporary Physics, 6 December 2013) "The monograph is applicable for courses on multivariate statistics for imaging science, optics, and photonics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals working in imaging, optics, and photonics who carry out data analyses in their everyday work." (Zentralblatt MATH, 1 August 2013) Table of ContentsPreface xiii 1 Introduction 1 1.1 Who Should Read This Book 6 1.2 How This Book is Organized 6 1.3 How to Read This Book and Learn from It 7 1.4 Note for Instructors 8 1.5 Book Web Site 9 2 Fundamentals of Statistics 11 2.1 Statistical Thinking 11 2.2 Data Format 13 2.3 Descriptive Statistics 14 2.3.1 Measures of Location 14 2.3.2 Measures of Variability 16 2.4 Data Visualization 17 2.4.1 Dot Plots 17 2.4.2 Histograms 19 2.4.3 Box Plots 23 2.4.4 Scatter Plots 24 2.5 Probability and Probability Distributions 26 2.5.1 Probability and Its Properties 26 2.5.2 Probability Distributions 30 2.5.3 Expected Value and Moments 33 2.5.4 Joint Distributions and Independence 34 2.5.5 Covariance and Correlation 38 2.6 Rules of Two and Three Sigma 40 2.7 Sampling Distributions and the Laws of Large Numbers 41 2.8 Skewness and Kurtosis 44 3 Statistical Inference 51 3.1 Introduction 51 3.2 Point Estimation of Parameters 53 3.2.1 Definition and Properties of Estimators 53 3.2.2 The Method of the Moments and Plug-In Principle 56 3.2.3 The Maximum Likelihood Estimation 57 3.3 Interval Estimation 60 3.4 Hypothesis Testing 63 3.5 Samples From Two Populations 71 3.6 Probability Plots and Testing for Population Distributions 73 3.6.1 Probability Plots 74 3.6.2 Kolmogorov–Smirnov Statistic 75 3.6.3 Chi-Squared Test 76 3.6.4 Ryan–Joiner Test for Normality 76 3.7 Outlier Detection 77 3.8 Monte Carlo Simulations 79 3.9 Bootstrap 79 4 Statistical Models 85 4.1 Introduction 85 4.2 Regression Models 85 4.2.1 Simple Linear Regression Model 86 4.2.2 Residual Analysis 94 4.2.3 Multiple Linear Regression and Matrix Notation 96 4.2.4 Geometric Interpretation in an n-Dimensional Space 99 4.2.5 Statistical Inference in Multiple Linear Regression 100 4.2.6 Prediction of the Response and Estimation of the Mean Response 104 4.2.7 More on Checking the Model Assumptions 107 4.2.8 Other Topics in Regression 110 4.3 Experimental Design and Analysis 111 4.3.1 Analysis of Designs with Qualitative Factors 116 4.3.2 Other Topics in Experimental Design 124 Supplement 4A. Vector and Matrix Algebra 125 Vectors 125 Matrices 127 Eigenvalues and Eigenvectors of Matrices 130 Spectral Decomposition of Matrices 130 Positive Definite Matrices 131 A Square Root Matrix 131 Supplement 4B. Random Vectors and Matrices 132 Sphering 134 5 Fundamentals of Multivariate Statistics 137 5.1 Introduction 137 5.2 The Multivariate Random Sample 139 5.3 Multivariate Data Visualization 143 5.4 The Geometry of the Sample 148 5.4.1 The Geometric Interpretation of the Sample Mean 148 5.4.2 The Geometric Interpretation of the Sample Standard Deviation 149 5.4.3 The Geometric Interpretation of the Sample Correlation Coefficient 150 5.5 The Generalized Variance 151 5.6 Distances in the p-Dimensional Space 159 5.7 The Multivariate Normal (Gaussian) Distribution 163 5.7.1 The Definition and Properties of the Multivariate Normal Distribution 163 5.7.2 Properties of the Mahalanobis Distance 166 6 Multivariate Statistical Inference 173 6.1 Introduction 173 6.2 Inferences About a Mean Vector 173 6.2.1 Testing the Multivariate Population Mean 173 6.2.2 Interval Estimation for the Multivariate Population Mean 175 6.2.3 T 2 Confidence Regions 179 6.3 Comparing Mean Vectors from Two Populations 183 6.3.1 Equal Covariance Matrices 184 6.3.2 Unequal Covariance Matrices and Large Samples 185 6.3.3 Unequal Covariance Matrices and Samples Sizes Not So Large 186 6.4 Inferences About a Variance–Covariance Matrix 187 6.5 How to Check Multivariate Normality 188 7 Principal Component Analysis 193 7.1 Introduction 193 7.2 Definition and Properties of Principal Components 195 7.2.1 Definition of Principal Components 195 7.2.2 Finding Principal Components 196 7.2.3 Interpretation of Principal Component Loadings 200 7.2.4 Scaling of Variables 207 7.3 Stopping Rules for Principal Component Analysis 209 7.3.1 Fair-Share Stopping Rules 210 7.3.2 Large-Gap Stopping Rules 213 7.4 Principal Component Scores 217 7.5 Residual Analysis 220 7.6 Statistical Inference in Principal Component Analysis 227 7.6.1 Independent and Identically Distributed Observations 227 7.6.2 Imaging Related Sampling Schemes 228 7.7 Further Reading 238 8 Canonical Correlation Analysis 241 8.1 Introduction 241 8.2 Mathematical Formulation 242 8.3 Practical Application 245 8.4 Calculating Variability Explained by Canonical Variables 246 8.5 Canonical Correlation Regression 251 8.6 Further Reading 256 Supplement 8A. Cross-Validation 256 9 Discrimination and Classification – Supervised Learning 261 9.1 Introduction 261 9.2 Classification for Two Populations 264 9.2.1 Classification Rules for Multivariate Normal Distributions 267 9.2.2 Cross-Validation of Classification Rules 277 9.2.3 Fisher’s Discriminant Function 280 9.3 Classification for Several Populations 284 9.3.1 Gaussian Rules 284 9.3.2 Fisher’s Method 286 9.4 Spatial Smoothing for Classification 291 9.5 Further Reading 293 10 Clustering – Unsupervised Learning 297 10.1 Introduction 297 10.2 Similarity and Dissimilarity Measures 298 10.2.1 Similarity and Dissimilarity Measures for Observations 298 10.2.2 Similarity and Dissimilarity Measures for Variables and Other Objects 304 10.3 Hierarchical Clustering Methods 304 10.3.1 Single Linkage Algorithm 305 10.3.2 Complete Linkage Algorithm 312 10.3.3 Average Linkage Algorithm 315 10.3.4 Ward Method 319 10.4 Nonhierarchical Clustering Methods 320 10.4.1 K-Means Method 320 10.5 Clustering Variables 323 10.6 Further Reading 325 Appendix A Probability Distributions 329 Appendix B Data Sets 349 Appendix C Miscellanea 355 References 365 Index 371

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Book SynopsisThis book provides an introduction to both Bayesian methods and gene expression, accessible to people with backgrounds in either. The text is enhanced by the inclusion of numerous problems and solutions, designed with an emphasis on methodology and application.Trade Review“The target audience for this book is clearly statisticians rather than biologists … It does provide a very useful overview of statistical genomics for anyone working in the field.” (The Quarterly Review of Biology, 1 March 2012) "Bioinformatics researchers from many fields will find much value in this book." (Mathematical Reviews, 2011) "Experienced readers will find the review of advanced methods for bioinformatics challenging and attainable. This book will interest graduate students in statistics and bioinformatics researchers from many fields." (Book News, December 2009)Table of ContentsTable of Notation. 1 Bioinformatics and Gene Expression Experiments. 1.1 Introduction. 1.2 About This Book. 2 Basic Biology. 2.1 Background. 2.1.1 DNA Structures and Transcription. 2.2 Gene Expression Microarray Experiments. 3 Bayesian Linear Models for Gene Expression. 3.1 Introduction. 3.2 Bayesian Analysis of a Linear Model. 3.3 Bayesian Linear Models for Differential Expression. 3.4 Bayesian ANOVA for Gene Selection. 3.5 Robust ANOVA model with Mixtures of Singular Distributions. 3.6 Case Study. 3.7 Accounting for Nuisance Effects. 3.8 Summary and Further Reading. 4 Bayesian Multiple Testing and False Discovery Rate Analysis. 4.1 Introduction to Multiple Testing. 4.2 False Discovery Rate Analysis. 4.3 Bayesian False Discovery Rate Analysis. 4.4 Bayesian Estimation of FDR. 4.5 FDR and Decision Theory. 4.6 FDR and bFDR Summary. 5 Bayesian Classification for Microarray Data. 5.1 Introduction. 5.2 Classification and Discriminant Rules. 5.3 Bayesian Discriminant Analysis. 5.4 Bayesian Regression Based Approaches to Classification. 5.5 Bayesian Nonlinear Classification. 5.6 Prediction and Model Choice. 5.7 Examples. 5.8 Discussion. 6 Bayesian Hypothesis Inference for Gene Classes. 6.1 Interpreting Microarray Results. 6.2 Gene Classes. 6.3 Bayesian Enrichment Analysis. 6.4 Multivariate Gene Class Detection. 6.5 Summary. 7 Unsupervised Classification and Bayesian Clustering. 7.1 Introduction to Bayesian Clustering for Gene Expression Data. 7.2 Hierarchical Clustering. 7.3 K-Means Clustering. 7.4 Model-Based Clustering. 7.5 Model-Based Agglomerative Hierarchical Clustering. 7.6 Bayesian Clustering. 7.7 Principal Components. 7.8 Mixture Modeling. 7.8.1 Label Switching. 7.9 Clustering Using Dirichlet Process Prior. 7.9.1 Infinite Mixture of Gaussian Distributions. 8 Bayesian Graphical Models. 8.1 Introduction. 8.2 Probabilistic Graphical Models. 8.3 Bayesian Networks. 8.4 Inference for Network Models. 9 Advanced Topics. 9.1 Introduction. 9.2 Analysis of Time Course Gene Expression Data. 9.3 Survival Prediction Using Gene Expression Data. Appendix A: Basics of Bayesian Modeling. A.1 Basics. A.1.1 The General Representation Theorem. A.1.2 Bayes’ Theorem. A.1.3 Models Based on Partial Exchangeability. A.1.4 Modeling with Predictors. A.1.5 Prior Distributions. A.1.6 Decision Theory and Posterior and Predictive Inferences. A.1.7 Predictive Distributions. A.1.8 Examples. A.2 Bayesian Model Choice. A.3 Hierarchical Modeling. A.4 Bayesian Mixture Modeling. A.5 Bayesian Model Averaging. Appendix B: Bayesian Computation Tools. B.1 Overview. B.2 Large-Sample Posterior Approximations. B.2.1 The Bayesian Central Limit Theorem. B.2.2 Laplace’s Method. B.3 Monte Carlo Integration. B.4 Importance Sampling. B.5 Rejection Sampling. B.6 Gibbs Sampling. B.7 The Metropolis Algorithm and Metropolis–Hastings. B.8 Advanced Computational Methods. B.8.1 Block MCMC. B.8.2 Truncated Posterior Spaces. B.8.3 Latent Variables and the Auto-Probit Model. B.8.4 Bayesian Simultaneous Credible Envelopes. B.8.5 Proposal Updating. B.9 Posterior Convergence Diagnostics. B.10 MCMC Convergence and the Proposal. B.10.1 Graphical Checks for MCMC Methods. B.10.2 Convergence Statistics. B.10.3 MCMC in High-Throughput Analysis. B.11 Summary. References. Index.

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Book SynopsisThis book provides a modern, hands-on guide to the essential concepts and ideas for analyzing data with missing observations in the field of biostatistics. It acknowledges the limitations of established techniques and provides concrete applications of newly developed methods.Trade Review“Overall the book is an excellent reference for biostatisticians who are interested in methodological approaches as well as for biostatisticians who prefer the applied side. Several useful examples from clinical trials and health research are carefully selected and analyzed to demonstrate the methods covered in the book. It is also a useful resource for postgraduate students researching missing-data methods and their application.” (Biometrical Journal, 1 June 2015) Table of Contents1 Missing Data Concepts and Motivating Examples 1 2 Overview of Methods for Dealing with Missing Data 15 3 Design Considerations in the Presence Of Missing Data 25 4 Cross-sectional Data Methods 31 5 Longitudinal Data Methods 69 6 Survival Analysis Under Ignorable Missingness 121 7 Nonignorable Missingness 147 8 Analysis of Randomized Clinical Trials With Noncompliance 185 Bibliography 215 Index 225

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Book SynopsisThis book is a comprehensive treatment of correlation/regression techniques and using SPSS for interpretation of findings. Striking a balance between detailed coverage and approachability, this book provides a thorough treatment of the elements of regression and how they can be used with real research problems in program evaluation. The author begins with a basic introduction to evaluation methodology, and its ability to recognize embedded patterns of meaning in research data. Subsequent chapters explore the statistical tools that can be applied by researchers and evaluators irrespective of the design that was used to generate this data. Topics of coverage include: correlation, single predictor regression, multiple correlation, part and partial correlation, detection of extreme scores, multiple regression, regression with continuous predictors, coding of categorical data, regression with categorical predictors, methods for entering predictors in multiple regression, and inteTable of ContentsCHAPTER ONE: INTRODUCTION. Initial Considerations. Book Plan. Real Examples. Using Statistical Programs. The Evaluator’s Journey. CHAPTER TWO: THE ELEMENTS OF EVALUATION. Nature of Evaluation. Evaluation Concerns. Evaluation Standards. Methods used in Evaluation. The Evaluator’s Tools. Evaluation Hurdles. Quantification. Resistance to Quantification. The Nature of Quantification. Qualitative Methods. Specialization. Statistical Issues. Certainty vs. Probability. Statistical Significance. Effect Sizes. Can We Achieve Certainty? Dispelling the Mystique of Statistics. Research Literacy. The Discovery Questions. School Characteristics and Student Learning. Worker Participation. The Impact of Technology on the Classroom. Classroom Observation Data. Discovery Learning. Terms and Concepts. CHAPTER THREE: Using SPSS? General Features. Management Functions. Reading and Importing Data. Sort. Split File. Transform/compute (creating indices). Merge. Analysis Functions. Graphing Functions. CHAPTER FOUR: CORRELATION. The Nature of Correlation. Prediction. Correlation is not Causation. Pearson’s r. Strength and Direction. A Note on the Nature of the Data. Interpreting Pearson’s r. Testing the Statistical Significance of a Correlation. The "Practical Significance" of r: Effect Sizes. An Evaluation Example of Correlation: The Impact of Technology on Teaching and Learning. Influences on Correlation. Restricted Range. Extreme (outlier) Scores. Other Kinds of Correlation. A Research Example of Spearman’s rho Correlation. Non Linear Correlation. "Extending" Correlation to Include Additional Variables. Correlation - Detail for the Curious. Computing Pearson’s r. Assumptions of Correlation. Non-Linear Correlation. Discovery Learning. Terms and Concepts. Practical Application-Correlation. Description of the Data. Evaluation Questions. CHAPTER FIVE: REGRESSION. The Regression Line - Line of "Best Fit". The Regression Formula. Standard Error of Estimate. Confidence Interval. Residuals. Regression Example with Achievement Data. The Results of the Analysis. The Graph of the Results. Standard Error of Estimate. The Confidence Interval. Detail - for the curious. Assumptions of Regression. Fixed vs. Random Effects Modeling. Non-Linear Correlation. Calculating the Standard Error of the Estimate. Discovery Note. Terms and Concepts. Practical Application - Bivariate Regression. CHAPTER SIX: CLEANING THE DATA - DETECTING OUTLIERS. Univariate Extreme Scores. Multivariate Extreme Scores. Distance Statistics. Influence Statistics. Discovery Note. Terms and Concepts. Practical Application - Extreme Scores. CHAPTER SEVEN: MULTIPLE CORRELATION. Introduction. Control Variables. Mediator Variables. Using Multiple Correlation to Control Variables: Partial & Semi-partial correlation. Partial Correlation. Semi-partial (Part) Correlation. Discovery Note. Terms and Concepts. Practical Application - Partial and Semi-Partial Correlation. CHAPTER EIGHT: MULTIPLE REGRESSION. Multiple Regression With Two Predictor Variables. Uses of Multiple Regression. Multiple Regression Outcomes. Omnibus Findings for the Overall Model. Individual Predictors. Additional SPSS® Results. Multiple Regression: How to Enter Predictors. Stepwise Regression and Other Methods. Assumptions of Multiple Regression. Multicollinearity. Cleaning the Database. Multiple Regression with More Than Two Predictor Variables: Research Examples. Predicting the Impact of School Variables on Teaching and Learning: the TAGLIT Data. Omnibus Findings. Results of Individual Predictors. Discovery Notes. Terms and Concepts. Practical Application: Multiple Regression. CHAPTER NINE: CODING - USING MLR WITH CATEGORICAL VARIABLES. Nature of Dummy Variables. One Categorical Variable with Two Groups. Creating Dummy Variables. Creating Subvariables in SPSS®. One Categorical Variable with More Than Two Groups. A Hypothetical Example. An Example from the School Database. Discovery Notes. Detail for the Curious. False Dichotomies. Discovery Note. Terms and Concepts. Practical Application: Dummy Coding. CHAPTER TEN: INTERACTION. Interactions with Continuous Variables. Interaction with Categorical Variables. Discovery Notes. Terms and Concepts. Practical Application - Interaction. CHAPTER ELEVEN: DISCOVERY LEARNING THROUGH CORRELATION AND REGRESSION. Overall Discovery Notes. Findings from the Data. Student Academic Achievement. Workplace Participation. The Impact of Technology on Student Learning. Advanced Statistical Techniques. Hierarchical Linear Regression. Structural Equation Modeling and Path Analysis. Other Regression Procedures. CHAPTER TWELVE: PRACTICAL APPLICATION ANALYSES. Practical Application: Correlation. Practical Application: Bivariate Regression. Practical Application: Extreme Scores. Practical Application: Partial and Semi-Partial Correlation. Practical Application: Multiple Regression. Practical Application: Dummy Coding. Practical Application: Interaction. REFERENCES.

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Book SynopsisQuantitative and Statistical Research Methods This user-friendly textbook teaches students to understand and apply procedural steps in completing quantitative studies. It explains statistics while progressing through the steps of the hypothesis-testing process from hypothesis to results. The research problems used in the book reflect statistical applications related to interesting and important topics. In addition, the book provides a Research Analysis and Interpretation Guide to help students analyze research articles. Designed as a hands-on resource, each chapter covers a single research problem and offers directions for implementing the research method from start to finish. Readers will learn how to: Pinpoint research questions and hypotheses Identify, classify, and operationally define the study variables Choose appropriate research designs Conduct power analysis Select an appropriate statistic for the problem <Table of ContentsTables and Figures ix Preface xvii The Authors xix Chapter 1 Introduction and Overview 1 Review of Foundational Research Concepts 3 Review of Foundational Statistical Information 6 The Normal Distribution 14 Chapter 2 Logical Steps of Conducting Quantitative Research: Hypothesis-Testing Process 29 Hypothesis-Testing Process 30 Chapter 3 Maximizing Hypothesis Decisions Using Power Analysis 39 Balance between Avoiding Type I and Type II Errors 41 Chapter 4 Research and Statistical Designs 53 Formulating Experimental Conditions 54 Reducing the Imprecision in Measurement 55 Controlling Extraneous Experimental Influences 57 Internal Validity and Experimental Designs 59 Choosing a Statistic to Use for an Analysis 67 Chapter 5 Introduction to IBM SPSS 20 77 The IBM SPSS 20 Data View Screen 80 Naming and Defining Variables in Variable View 80 Entering Data 86 Examples of Basic Analyses 87 Examples of Modifying Data Procedures 96 Chapter 6 Diagnosing Study Data for Inaccuracies and Assumptions 99 Research Example 100 Chapter 7 Randomized Design Comparing Two Treatments and a Control Using a One-Way Analysis of Variance 129 Research Problem 130 Study Variables 131 Research Design 133 Stating the Omnibus (Comprehensive) Research Question 135 Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha) 136 Hypothesis Testing Step 2: Establish the Null Hypothesis (H0) 137 Hypothesis Testing Step 3: Decide on a Risk Level (Alpha) of Rejecting the True H0 Considering Type I and II Errors and Power 138 Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 Is True 143 Hypothesis Testing Step 5: Select Sample, Collect Data, Screen Data, Compute Statistic, and Determine Probability Estimates 144 Hypothesis Testing Step 6: Make Decision Regarding the H0 and Interpret Post Hoc Effect Sizes and Confidence Intervals 162 Formula Calculations of the Study Results 166 Chapter 8 Repeated-Treatment Design Using a Repeated-Measures Analysis of Variance 183 Research Problem 184 Study Variables 185 Research Design 186 Stating the Omnibus (Comprehensive) Research Question 189 Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha) 190 Hypothesis Testing Step 2: Establish the Null Hypothesis (H0) 191 Hypothesis Testing Step 3: Decide on a Risk Level (Alpha) of Rejecting the True H0 Considering Type I and II Errors and Power 192 Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 Is True 195 Hypothesis Testing Step 5: Select Sample, Collect Data, Screen Data, Compute Statistic, and Determine Probability Estimates 196 Hypothesis Testing Step 6: Make Decision Regarding the H0 and Interpret Post Hoc Effect Sizes and Confidence Intervals 216 Formula Calculations of the Study Results 218 Chapter 9 Randomized Factorial Experimental Design Using a Factorial ANOVA 231 Research Problem 232 Study Variables 232 Research Design 233 Stating the Omnibus (Comprehensive) Research Questions 237 Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha) 238 Hypothesis Testing Step 2: Establish the Null Hypothesis (H0) 240 Hypothesis Testing Step 3: Decide on a Risk Level (Alpha) of Rejecting the True H0 Considering Type I and II Errors and Power 241 Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 Is True 247 Hypothesis Testing Step 5: Select Sample, Collect Data, Screen Data, Compute Statistic, and Determine Probability Estimates 248 Hypothesis Testing Step 6: Make Decision Regarding the H0 and Interpret Post Hoc Effect Sizes and Confidence Intervals 271 Formula Calculations of the Study Results 278 Chapter 10 Analysis of Covariance 297 Research Problem 298 Study Variables 299 Research Design 300 Stating the Omnibus (Comprehensive) Research Question 301 Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha) 301 Hypothesis Testing Step 2: Establish the Null Hypothesis (H0) 302 Hypothesis Testing Step 3: Decide on a Risk Level (Alpha) of Rejecting the True H0 Considering Type I and II Errors and Power 302 Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 is True 306 Hypothesis Testing Step 5: Select Sample, Collect Data, Screen Data, Compute Statistic, and Determine Probability Estimates 307 Hypothesis Testing Step 6: Make Decision Regarding the H0 and Interpret Post Hoc Effect Sizes and Confidence Intervals 324 Formula ANCOVA Calculations of the Study Results 327 ANCOVA Study Results 339 Chapter 11 Randomized Control Group and Repeated-Treatment Designs and Nonparametics 345 Research Problem 346 Study Variables 346 Research Design 347 Stating the Omnibus (Comprehensive) Research Question 349 Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha) 349 Hypothesis Testing Step 2: Establish the Null Hypothesis (H0) 350 Hypothesis Testing Step 3: Decide on a Risk Level (Alpha) of Rejecting the True H0 Considering Type I and II Errors and Power 350 Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 is True 354 Hypothesis Testing Step 5: Select Sample, Collect Data, Screen Data, Compute Statistic, and Determine Probability Estimates 355 Hypothesis Testing Step 6: Make Decision Regarding the H0 and Interpret Post Hoc Effect Sizes 370 Formula Calculations 376 Nonparametric Research Problem Two: Friedman’s Rank Test for Correlated Samples and Wilcoxon’s Matched-Pairs Signed-Ranks Test 382 Chapter 12 Bivariate and Multivariate Correlation Methods Using Multiple Regression Analysis 401 Research Problem 402 Study Variables 402 Research Method 403 Stating the Omnibus (Comprehensive) Research Question 405 Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha) 405 Hypothesis Testing Step 2: Establish the Null Hypothesis (H0) 406 Hypothesis Testing Step 3: Decide on a Risk Level (Alpha) of Rejecting the True H0 Considering Type I and II Errors and Power 406 Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 is True 407 Hypothesis Testing Step 5: Select Sample, Collect Data, Screen Data, Compute Statistic, and Determine Probability Estimates 407 Hand Calculations of Statistics 423 Chapter 13 Understanding Quantitative Literature and Research 439 Interpretation of a Quantitative Research Article 440 References 461 Index 465

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Book SynopsisStatistical pattern recognition relates to the use of statistical techniques for analysing data measurements in order to extract information and make justified decisions. It is a very active area of study and research, which has seen many advances in recent years.Trade Review"In the end I must add that this book is so appealing that I often found myself lost in the reading, pausing the overview of the manuscript in order to look more into some presented subject, and not being able to continue until I had finished seeing all about it.” (Zentralblatt MATH, 1 December 2012)Table of ContentsPreface xix Notation xxiii 1 Introduction to Statistical Pattern Recognition 1 1.1 Statistical Pattern Recognition 1 1.1.1 Introduction 1 1.1.2 The Basic Model 2 1.2 Stages in a Pattern Recognition Problem 4 1.3 Issues 6 1.4 Approaches to Statistical Pattern Recognition 7 1.5 Elementary Decision Theory 8 1.5.1 Bayes’ Decision Rule for Minimum Error 8 1.5.2 Bayes’ Decision Rule for Minimum Error – Reject Option 12 1.5.3 Bayes’ Decision Rule for Minimum Risk 13 1.5.4 Bayes’ Decision Rule for Minimum Risk – Reject Option 15 1.5.5 Neyman–Pearson Decision Rule 15 1.5.6 Minimax Criterion 18 1.5.7 Discussion 19 1.6 Discriminant Functions 20 1.6.1 Introduction 20 1.6.2 Linear Discriminant Functions 21 1.6.3 Piecewise Linear Discriminant Functions 23 1.6.4 Generalised Linear Discriminant Function 24 1.6.5 Summary 26 1.7 Multiple Regression 27 1.8 Outline of Book 29 1.9 Notes and References 29 Exercises 31 2 Density Estimation – Parametric 33 2.1 Introduction 33 2.2 Estimating the Parameters of the Distributions 34 2.2.1 Estimative Approach 34 2.2.2 Predictive Approach 35 2.3 The Gaussian Classifier 35 2.3.1 Specification 35 2.3.2 Derivation of the Gaussian Classifier Plug-In Estimates 37 2.3.3 Example Application Study 39 2.4 Dealing with Singularities in the Gaussian Classifier 40 2.4.1 Introduction 40 2.4.2 Na¨ive Bayes 40 2.4.3 Projection onto a Subspace 41 2.4.4 Linear Discriminant Function 41 2.4.5 Regularised Discriminant Analysis 42 2.4.6 Example Application Study 44 2.4.7 Further Developments 45 2.4.8 Summary 46 2.5 Finite Mixture Models 46 2.5.1 Introduction 46 2.5.2 Mixture Models for Discrimination 48 2.5.3 Parameter Estimation for Normal Mixture Models 49 2.5.4 Normal Mixture Model Covariance Matrix Constraints 51 2.5.5 How Many Components? 52 2.5.6 Maximum Likelihood Estimation via EM 55 2.5.7 Example Application Study 60 2.5.8 Further Developments 62 2.5.9 Summary 63 2.6 Application Studies 63 2.7 Summary and Discussion 66 2.8 Recommendations 66 2.9 Notes and References 67 Exercises 67 3 Density Estimation – Bayesian 70 3.1 Introduction 70 3.1.1 Basics 72 3.1.2 Recursive Calculation 72 3.1.3 Proportionality 73 3.2 Analytic Solutions 73 3.2.1 Conjugate Priors 73 3.2.2 Estimating the Mean of a Normal Distribution with Known Variance 75 3.2.3 Estimating the Mean and the Covariance Matrix of a Multivariate Normal Distribution 79 3.2.4 Unknown Prior Class Probabilities 85 3.2.5 Summary 87 3.3 Bayesian Sampling Schemes 87 3.3.1 Introduction 87 3.3.2 Summarisation 87 3.3.3 Sampling Version of the Bayesian Classifier 89 3.3.4 Rejection Sampling 89 3.3.5 Ratio of Uniforms 90 3.3.6 Importance Sampling 92 3.4 Markov Chain Monte Carlo Methods 95 3.4.1 Introduction 95 3.4.2 The Gibbs Sampler 95 3.4.3 Metropolis–Hastings Algorithm 103 3.4.4 Data Augmentation 107 3.4.5 Reversible Jump Markov Chain Monte Carlo 108 3.4.6 Slice Sampling 109 3.4.7 MCMC Example – Estimation of Noisy Sinusoids 111 3.4.8 Summary 115 3.4.9 Notes and References 116 3.5 Bayesian Approaches to Discrimination 116 3.5.1 Labelled Training Data 116 3.5.2 Unlabelled Training Data 117 3.6 Sequential Monte Carlo Samplers 119 3.6.1 Introduction 119 3.6.2 Basic Methodology 121 3.6.3 Summary 125 3.7 Variational Bayes 126 3.7.1 Introduction 126 3.7.2 Description 126 3.7.3 Factorised Variational Approximation 129 3.7.4 Simple Example 131 3.7.5 Use of the Procedure for Model Selection 135 3.7.6 Further Developments and Applications 136 3.7.7 Summary 137 3.8 Approximate Bayesian Computation 137 3.8.1 Introduction 137 3.8.2 ABC Rejection Sampling 138 3.8.3 ABC MCMC Sampling 140 3.8.4 ABC Population Monte Carlo Sampling 141 3.8.5 Model Selection 142 3.8.6 Summary 143 3.9 Example Application Study 144 3.10 Application Studies 145 3.11 Summary and Discussion 146 3.12 Recommendations 147 3.13 Notes and References 147 Exercises 148 4 Density Estimation – Nonparametric 150 4.1 Introduction 150 4.1.1 Basic Properties of Density Estimators 150 4.2 k-Nearest-Neighbour Method 152 4.2.1 k-Nearest-Neighbour Classifier 152 4.2.2 Derivation 154 4.2.3 Choice of Distance Metric 157 4.2.4 Properties of the Nearest-Neighbour Rule 159 4.2.5 Linear Approximating and Eliminating Search Algorithm 159 4.2.6 Branch and Bound Search Algorithms: kd-Trees 163 4.2.7 Branch and Bound Search Algorithms: Ball-Trees 170 4.2.8 Editing Techniques 174 4.2.9 Example Application Study 177 4.2.10 Further Developments 178 4.2.11 Summary 179 4.3 Histogram Method 180 4.3.1 Data Adaptive Histograms 181 4.3.2 Independence Assumption (Na¨ive Bayes) 181 4.3.3 Lancaster Models 182 4.3.4 Maximum Weight Dependence Trees 183 4.3.5 Bayesian Networks 186 4.3.6 Example Application Study – Na¨ive Bayes Text Classification 190 4.3.7 Summary 193 4.4 Kernel Methods 194 4.4.1 Biasedness 197 4.4.2 Multivariate Extension 198 4.4.3 Choice of Smoothing Parameter 199 4.4.4 Choice of Kernel 201 4.4.5 Example Application Study 202 4.4.6 Further Developments 203 4.4.7 Summary 203 4.5 Expansion by Basis Functions 204 4.6 Copulas 207 4.6.1 Introduction 207 4.6.2 Mathematical Basis 207 4.6.3 Copula Functions 208 4.6.4 Estimating Copula Probability Density Functions 209 4.6.5 Simple Example 211 4.6.6 Summary 212 4.7 Application Studies 213 4.7.1 Comparative Studies 216 4.8 Summary and Discussion 216 4.9 Recommendations 217 4.10 Notes and References 217 Exercises 218 5 Linear Discriminant Analysis 221 5.1 Introduction 221 5.2 Two-Class Algorithms 222 5.2.1 General Ideas 222 5.2.2 Perceptron Criterion 223 5.2.3 Fisher’s Criterion 227 5.2.4 Least Mean-Squared-Error Procedures 228 5.2.5 Further Developments 235 5.2.6 Summary 235 5.3 Multiclass Algorithms 236 5.3.1 General Ideas 236 5.3.2 Error-Correction Procedure 237 5.3.3 Fisher’s Criterion – Linear Discriminant Analysis 238 5.3.4 Least Mean-Squared-Error Procedures 241 5.3.5 Regularisation 246 5.3.6 Example Application Study 246 5.3.7 Further Developments 247 5.3.8 Summary 248 5.4 Support Vector Machines 249 5.4.1 Introduction 249 5.4.2 Linearly Separable Two-Class Data 249 5.4.3 Linearly Nonseparable Two-Class Data 253 5.4.4 Multiclass SVMs 256 5.4.5 SVMs for Regression 257 5.4.6 Implementation 259 5.4.7 Example Application Study 262 5.4.8 Summary 263 5.5 Logistic Discrimination 263 5.5.1 Two-Class Case 263 5.5.2 Maximum Likelihood Estimation 264 5.5.3 Multiclass Logistic Discrimination 266 5.5.4 Example Application Study 267 5.5.5 Further Developments 267 5.5.6 Summary 268 5.6 Application Studies 268 5.7 Summary and Discussion 268 5.8 Recommendations 269 5.9 Notes and References 270 Exercises 270 6 Nonlinear Discriminant Analysis – Kernel and Projection Methods 274 6.1 Introduction 274 6.2 Radial Basis Functions 276 6.2.1 Introduction 276 6.2.2 Specifying the Model 278 6.2.3 Specifying the Functional Form 278 6.2.4 The Positions of the Centres 279 6.2.5 Smoothing Parameters 281 6.2.6 Calculation of the Weights 282 6.2.7 Model Order Selection 284 6.2.8 Simple RBF 285 6.2.9 Motivation 286 6.2.10 RBF Properties 288 6.2.11 Example Application Study 288 6.2.12 Further Developments 289 6.2.13 Summary 290 6.3 Nonlinear Support Vector Machines 291 6.3.1 Introduction 291 6.3.2 Binary Classification 291 6.3.3 Types of Kernel 292 6.3.4 Model Selection 293 6.3.5 Multiclass SVMs 294 6.3.6 Probability Estimates 294 6.3.7 Nonlinear Regression 296 6.3.8 Example Application Study 296 6.3.9 Further Developments 297 6.3.10 Summary 298 6.4 The Multilayer Perceptron 298 6.4.1 Introduction 298 6.4.2 Specifying the MLP Structure 299 6.4.3 Determining the MLP Weights 300 6.4.4 Modelling Capacity of the MLP 307 6.4.5 Logistic Classification 307 6.4.6 Example Application Study 310 6.4.7 Bayesian MLP Networks 311 6.4.8 Projection Pursuit 313 6.4.9 Summary 313 6.5 Application Studies 314 6.6 Summary and Discussion 316 6.7 Recommendations 317 6.8 Notes and References 318 Exercises 318 7 Rule and Decision Tree Induction 322 7.1 Introduction 322 7.2 Decision Trees 323 7.2.1 Introduction 323 7.2.2 Decision Tree Construction 326 7.2.3 Selection of the Splitting Rule 327 7.2.4 Terminating the Splitting Procedure 330 7.2.5 Assigning Class Labels to Terminal Nodes 332 7.2.6 Decision Tree Pruning – Worked Example 332 7.2.7 Decision Tree Construction Methods 337 7.2.8 Other Issues 339 7.2.9 Example Application Study 340 7.2.10 Further Developments 341 7.2.11 Summary 342 7.3 Rule Induction 342 7.3.1 Introduction 342 7.3.2 Generating Rules from a Decision Tree 345 7.3.3 Rule Induction Using a Sequential Covering Algorithm 345 7.3.4 Example Application Study 350 7.3.5 Further Developments 351 7.3.6 Summary 351 7.4 Multivariate Adaptive Regression Splines 351 7.4.1 Introduction 351 7.4.2 Recursive Partitioning Model 351 7.4.3 Example Application Study 355 7.4.4 Further Developments 355 7.4.5 Summary 356 7.5 Application Studies 356 7.6 Summary and Discussion 358 7.7 Recommendations 358 7.8 Notes and References 359 Exercises 359 8 Ensemble Methods 361 8.1 Introduction 361 8.2 Characterising a Classifier Combination Scheme 362 8.2.1 Feature Space 363 8.2.2 Level 366 8.2.3 Degree of Training 368 8.2.4 Form of Component Classifiers 368 8.2.5 Structure 369 8.2.6 Optimisation 369 8.3 Data Fusion 370 8.3.1 Architectures 370 8.3.2 Bayesian Approaches 371 8.3.3 Neyman–Pearson Formulation 373 8.3.4 Trainable Rules 374 8.3.5 Fixed Rules 375 8.4 Classifier Combination Methods 376 8.4.1 Product Rule 376 8.4.2 Sum Rule 377 8.4.3 Min, Max and Median Combiners 378 8.4.4 Majority Vote 379 8.4.5 Borda Count 379 8.4.6 Combiners Trained on Class Predictions 380 8.4.7 Stacked Generalisation 382 8.4.8 Mixture of Experts 382 8.4.9 Bagging 385 8.4.10 Boosting 387 8.4.11 Random Forests 389 8.4.12 Model Averaging 390 8.4.13 Summary of Methods 396 8.4.14 Example Application Study 398 8.4.15 Further Developments 399 8.5 Application Studies 399 8.6 Summary and Discussion 400 8.7 Recommendations 401 8.8 Notes and References 401 Exercises 402 9 Performance Assessment 404 9.1 Introduction 404 9.2 Performance Assessment 405 9.2.1 Performance Measures 405 9.2.2 Discriminability 406 9.2.3 Reliability 413 9.2.4 ROC Curves for Performance Assessment 415 9.2.5 Population and Sensor Drift 419 9.2.6 Example Application Study 421 9.2.7 Further Developments 422 9.2.8 Summary 423 9.3 Comparing Classifier Performance 424 9.3.1 Which Technique is Best? 424 9.3.2 Statistical Tests 425 9.3.3 Comparing Rules When Misclassification Costs are Uncertain 426 9.3.4 Example Application Study 428 9.3.5 Further Developments 429 9.3.6 Summary 429 9.4 Application Studies 429 9.5 Summary and Discussion 430 9.6 Recommendations 430 9.7 Notes and References 430 Exercises 431 10 Feature Selection and Extraction 433 10.1 Introduction 433 10.2 Feature Selection 435 10.2.1 Introduction 435 10.2.2 Characterisation of Feature Selection Approaches 439 10.2.3 Evaluation Measures 440 10.2.4 Search Algorithms for Feature Subset Selection 449 10.2.5 Complete Search – Branch and Bound 450 10.2.6 Sequential Search 454 10.2.7 Random Search 458 10.2.8 Markov Blanket 459 10.2.9 Stability of Feature Selection 460 10.2.10 Example Application Study 462 10.2.11 Further Developments 462 10.2.12 Summary 463 10.3 Linear Feature Extraction 463 10.3.1 Principal Components Analysis 464 10.3.2 Karhunen–Lo`eve Transformation 475 10.3.3 Example Application Study 481 10.3.4 Further Developments 482 10.3.5 Summary 483 10.4 Multidimensional Scaling 484 10.4.1 Classical Scaling 484 10.4.2 Metric MDS 486 10.4.3 Ordinal Scaling 487 10.4.4 Algorithms 490 10.4.5 MDS for Feature Extraction 491 10.4.6 Example Application Study 492 10.4.7 Further Developments 493 10.4.8 Summary 493 10.5 Application Studies 493 10.6 Summary and Discussion 495 10.7 Recommendations 495 10.8 Notes and References 496 Exercises 497 11 Clustering 501 11.1 Introduction 501 11.2 Hierarchical Methods 502 11.2.1 Single-Link Method 503 11.2.2 Complete-Link Method 506 11.2.3 Sum-of-Squares Method 507 11.2.4 General Agglomerative Algorithm 508 11.2.5 Properties of a Hierarchical Classification 508 11.2.6 Example Application Study 509 11.2.7 Summary 509 11.3 Quick Partitions 510 11.4 Mixture Models 511 11.4.1 Model Description 511 11.4.2 Example Application Study 512 11.5 Sum-of-Squares Methods 513 11.5.1 Clustering Criteria 514 11.5.2 Clustering Algorithms 515 11.5.3 Vector Quantisation 520 11.5.4 Example Application Study 530 11.5.5 Further Developments 530 11.5.6 Summary 531 11.6 Spectral Clustering 531 11.6.1 Elementary Graph Theory 531 11.6.2 Similarity Matrices 534 11.6.3 Application to Clustering 534 11.6.4 Spectral Clustering Algorithm 535 11.6.5 Forms of Graph Laplacian 535 11.6.6 Example Application Study 536 11.6.7 Further Developments 538 11.6.8 Summary 538 11.7 Cluster Validity 538 11.7.1 Introduction 538 11.7.2 Statistical Tests 539 11.7.3 Absence of Class Structure 540 11.7.4 Validity of Individual Clusters 541 11.7.5 Hierarchical Clustering 542 11.7.6 Validation of Individual Clusterings 542 11.7.7 Partitions 543 11.7.8 Relative Criteria 543 11.7.9 Choosing the Number of Clusters 545 11.8 Application Studies 546 11.9 Summary and Discussion 549 11.10 Recommendations 551 11.11 Notes and References 552 Exercises 553 12 Complex Networks 555 12.1 Introduction 555 12.1.1 Characteristics 557 12.1.2 Properties 557 12.1.3 Questions to Address 559 12.1.4 Descriptive Features 560 12.1.5 Outline 560 12.2 Mathematics of Networks 561 12.2.1 Graph Matrices 561 12.2.2 Connectivity 562 12.2.3 Distance Measures 562 12.2.4 Weighted Networks 563 12.2.5 Centrality Measures 563 12.2.6 Random Graphs 564 12.3 Community Detection 565 12.3.1 Clustering Methods 565 12.3.2 Girvan–Newman Algorithm 568 12.3.3 Modularity Approaches 570 12.3.4 Local Modularity 571 12.3.5 Clique Percolation 573 12.3.6 Example Application Study 574 12.3.7 Further Developments 575 12.3.8 Summary 575 12.4 Link Prediction 575 12.4.1 Approaches to Link Prediction 576 12.4.2 Example Application Study 578 12.4.3 Further Developments 578 12.5 Application Studies 579 12.6 Summary and Discussion 579 12.7 Recommendations 580 12.8 Notes and References 580 Exercises 580 13 Additional Topics 581 13.1 Model Selection 581 13.1.1 Separate Training and Test Sets 582 13.1.2 Cross-Validation 582 13.1.3 The Bayesian Viewpoint 583 13.1.4 Akaike’s Information Criterion 583 13.1.5 Minimum Description Length 584 13.2 Missing Data 585 13.3 Outlier Detection and Robust Procedures 586 13.4 Mixed Continuous and Discrete Variables 587 13.5 Structural Risk Minimisation and the Vapnik–Chervonenkis Dimension 588 13.5.1 Bounds on the Expected Risk 588 13.5.2 The VC Dimension 589 References 591 Index 637

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Book SynopsisThe latest tools and techniques for pricing and risk management This book introduces readers to the use of copula functions to represent the dynamics of financial assets and risk factors, integrated temporal and cross-section applications.Table of ContentsPreface ix 1 Correlation Risk in Finance 1 1.1 Correlation Risk in Pricing and Risk Management 1 1.2 Implied vs Realized Correlation 3 1.3 Bottom-up vs Top-down Models 4 1.4 Copula Functions 4 1.5 Spatial and Temporal Dependence 5 1.6 Long-range Dependence 5 1.7 Multivariate GARCH Models 7 1.8 Copulas and Convolution 8 2 Copula Functions: The State of the Art 11 2.1 Copula Functions: The Basic Recipe 11 2.2 Market Co-movements 14 2.3 Delta Hedging Multivariate Digital Products 16 2.4 Linear Correlation 19 2.5 Rank Correlation 20 2.6 Multivariate Spearman’s Rho 22 2.7 Survival Copulas and Radial Symmetry 23 2.8 Copula Volume and Survival Copulas 24 2.9 Tail Dependence 27 2.10 Long/Short Correlation 27 2.11 Families of Copulas 29 2.11.1 Elliptical Copulas 29 2.11.2 Archimedean Copulas 31 2.12 Kendall Function 33 2.13 Exchangeability 34 2.14 Hierarchical Copulas 35 2.15 Conditional Probability and Factor Copulas 39 2.16 Copula Density and Vine Copulas 42 2.17 Dynamic Copulas 45 2.17.1 Conditional Copulas 45 2.17.2 Pseudo-copulas 46 3 Copula Functions and Asset Price Dynamics 49 3.1 The Dynamics of Speculative Prices 49 3.2 Copulas and Markov Processes: The DNO approach 51 3.2.1 The * and _ Product Operators 52 3.2.2 Product Operators and Markov Processes 55 3.2.3 Self-similar Copulas 58 3.2.4 Simulating Markov Chains with Copulas 62 3.3 Time-changed Brownian Copulas 63 3.3.1 CEV Clock Brownian Copulas 64 3.3.2 VG Clock Brownian Copulas 65 3.4 Copulas and Martingale Processes 66 3.4.1 C-Convolution 67 3.4.2 Markov Processes with Independent Increments 75 3.4.3 Markov Processes with Dependent Increments 78 3.4.4 Extracting Dependent Increments in Markov Processes 81 3.4.5 Martingale Processes 83 3.5 Multivariate Processes 86 3.5.1 Multivariate Markov Processes 86 3.5.2 Granger Causality and the Martingale Condition 88 4 Copula-based Econometrics of Dynamic Processes 91 4.1 Dynamic Copula Quantile Regressions 91 4.2 Copula-based Markov Processes: Non-linear Quantile Autoregression 93 4.3 Copula-based Markov Processes: Semi-parametric Estimation 99 4.4 Copula-based Markov Processes: Non-parametric Estimation 108 4.5 Copula-based Markov Processes: Mixing Properties 110 4.6 Persistence and Long Memory 113 4.7 C-convolution-based Markov Processes: The Likelihood Function 116 5 Multivariate Equity Products 121 5.1 Multivariate Equity Products 121 5.1.1 European Multivariate Equity Derivatives 122 5.1.2 Path-dependent Equity Derivatives 125 5.2 Recursions of Running Maxima and Minima 126 5.3 The Memory Feature 130 5.4 Risk-neutral Pricing Restrictions 132 5.5 Time-changed Brownian Copulas 133 5.6 Variance Swaps 135 5.7 Semi-parametric Pricing of Path-dependent Derivatives 136 5.8 The Multivariate Pricing Setting 137 5.9 H-Condition and Granger Causality 137 5.10 Multivariate Pricing Recursion 138 5.11 Hedging Multivariate Equity Derivatives 141 5.12 Correlation Swaps 144 5.13 The Term Structure of Multivariate Equity Derivatives 147 5.13.1 Altiplanos 148 5.13.2 Everest 150 5.13.3 Spread Options 150 6 Multivariate Credit Products 153 6.1 Credit Transfer Finance 153 6.1.1 Univariate Credit Transfer Products 154 6.1.2 Multivariate Credit Transfer Products 155 6.2 Credit Information: Equity vs CDS 158 6.3 Structural Models 160 6.3.1 Univariate Model: Credit Risk as a Put Option 160 6.3.2 Multivariate Model: Gaussian Copula 161 6.3.3 Large Portfolio Model: Vasicek Formula 163 6.4 Intensity-based Models 164 6.4.1 Univariate Model: Poisson and Cox Processes 165 6.4.2 Multivariate Model: Marshall–Olkin Copula 165 6.4.3 Homogeneous Model: Cuadras Aug´e Copula 167 6.5 Frailty Models 170 6.5.1 Multivariate Model: Archimedean Copulas 170 6.5.2 Large Portfolio Model: Sch¨onbucher Formula 171 6.6 Granularity Adjustment 171 6.7 Credit Portfolio Analysis 172 6.7.1 Semi-unsupervised Cluster Analysis: K-means 172 6.7.2 Unsupervised Cluster Analysis: Kohonen Self-organizing Maps 174 6.7.3 (Semi-)unsupervised Cluster Analysis: Hierarchical Correlation Model 175 6.8 Dynamic Analysis of Credit Risk Portfolios 176 7 Risk Capital Management 181 7.1 A Review of Value-at-Risk and Other Measures 181 7.2 Capital Aggregation and Allocation 185 7.2.1 Aggregation: C-Convolution 187 7.2.2 Allocation: Level Curves 189 7.2.3 Allocation with Constraints 191 7.3 Risk Measurement of Managed Portfolios 193 7.3.1 Henriksson–Merton Model 195 7.3.2 Semi-parametric Analysis of Managed Funds 200 7.3.3 Market-neutral Investments 201 7.4 Temporal Aggregation of Risk Measures 202 7.4.1 The Square-root Formula 203 7.4.2 Temporal Aggregation by C-convolution 203 8 Frontier Issues 207 8.1 Levy Copulas 207 8.2 Pareto Copulas 210 8.3 Semi-martingale Copulas 212 A Elements of Probability 215 A.1 Elements of Measure Theory 215 A.2 Integration 216 A.2.1 Expected Values and Moments 217 A.3 The Moment-generating Function or Laplace Transform 218 A.4 The Characteristic Function 219 A.5 Relevant Probability Distributions 219 A.6 Random Vectors and Multivariate Distributions 224 A.6.1 The Multivariate Normal Distribution 225 A.7 Infinite Divisibility 226 A.8 Convergence of Sequences of Random Variables 228 A.81 The Strong Law of Large Numbers 229 A.9 The Radon–Nikodym Derivative 229 A.10 Conditional Expectation 229 B Elements of Stochastic Processes Theory 231 B.1 Stochastic Processes 231 B.1.1 Filtrations 231 B.1.2 Stopping Times 232 B.2 Martingales 233 B.3 Markov Processes 234 B.4 L´evy Processes 237 B.4.1 Subordinators 240 B.5 Semi-martingales 240 References 245 Extra Reading 251 Index 259

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Book SynopsisThis bookisa completely revised and updated version of this invaluable text which allows science students to extend necessary skills and techniques, with the topics being developed through examples in science which are easily understood by students from a range of disciplines. The introductory approach eases students into the subject, progressing to cover topics relevant to first and second year study and support data analysis for final year projects. The revision of the material in the book has been matched, on the accompanying website, with the extensive use of video, providing worked answers to over 200 questions in the book plus additional tutorial support. The second edition has also improved the learning approach for key topic areas to make it even more accessible and user-friendly, making it a perfect resource for students of all abilities. The expanding website provides a wide range of support material, providing a study environment within which students can develop their iTable of ContentsPreface xi On-line Learning Support xv 1 Mathematics and Statistics in Science 1 1.1 Data and Information 2 1.2 Experimental Variation and Uncertainty 2 1.3 Mathematical Models in Science 4 2 Scientific Data 7 2.1 Scientific Numbers 8 2.2 Scientific Quantities 15 2.3 Chemical Quantities 20 2.4 Angular Measurements 31 3 Equations in Science 41 3.1 Basic Techniques 41 3.2 Rearranging Simple Equations 53 3.3 Symbols 63 3.4 Further Equations 68 3.5 Quadratic and Simultaneous Equations 78 4 Linear Relationships 87 4.1 Straight Line Graph 89 4.2 Linear Regression 99 4.3 Linearization 107 5 Logarithmic and Exponential Functions 113 5.1 Mathematics of e, ln and log 114 5.2 Exponential Growth and Decay 128 6 Rates of Change 145 6.1 Rate of Change 145 6.2 Differentiation 152 7 Statistics for Science 161 7.1 Analysing Replicate Data 162 7.2 Describing and Estimating 168 7.3 Frequency Statistics 176 7.4 Probability 190 7.5 Factorials, Permutations and Combinations 203 8 Distributions and Uncertainty 211 8.1 Normal Distribution 212 8.2 Uncertainties in Measurement 217 8.3 Presenting Uncertainty 224 8.4 Binomial and Poisson Distributions 230 9 Scientific Investigation 243 9.1 Scientific Systems 243 9.2 The ‘Scientific Method’ 245 9.3 Decision Making with Statistics 246 9.4 Hypothesis Testing 250 9.5 Selecting Analyses and Tests 256 10 t-tests and F-tests 261 10.1 One-sample t-tests 262 10.2 Two-sample t-tests 267 10.3 Paired t-tests 272 10.4 F-tests 274 11 ANOVA – Analysis of Variance 279 11.1 One-way ANOVA 279 11.2 Two-way ANOVA 286 11.3 Two-way ANOVA with Replication 290 11.4 ANOVA Post Hoc Testing 296 12 Non-parametric Tests for Medians 299 12.1 One-sample Wilcoxon Test 301 12.2 Two-sample Mann–Whitney U-test 305 12.3 Paired Wilcoxon Test 308 12.4 Kruskal–Wallis and Friedman Tests 311 13 Correlation and Regression 315 13.1 Linear Correlation 316 13.2 Statistics of Correlation and Regression 320 13.3 Uncertainty in Linear Calibration 324 14 Frequency and Proportion 331 14.1 Chi-squared Contingency Table 332 14.2 Goodness of Fit 340 14.3 Tests for Proportion 343 15 Experimental Design 349 15.1 Principal Techniques 349 15.2 Planning a Research Project 357 Appendix I: Microsoft Excel 359 Appendix II: Cumulative z-areas for Standard Normal Distribution 363 Appendix III: Critical Values: t-statistic and Chi-squared, χ2 365 Appendix IV: Critical F-values at 0.05 (95 %) Significance 367 Appendix V: Critical Values at 0.05 (95 %) Significance for: Pearson’s Correlation Coefficient, r, Spearman’s Rank Correlation Coefficient, rS , and Wilcoxon Lower Limit, WL 369 Appendix VI: Mann–Whitney Lower Limit, UL, at 0.05 (95 %) Significance 371 Short Answers to ‘Q’ Questions 373 Index 379

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Book SynopsisHow to Be a Quantitative Ecologist is comprised of two equal parts on mathematics and statistics with emphasis on quantitative skills. A major component of this guide is computer implementation techniques, accompanied by computer practicals using the language R.Trade Review“For those looking through R books for something a bit more technical, this book will be an essential accomplice to mastering R.” (British Ecological Society, 1 April 2013) “The book is written in a style that is easy to read and for which one quickly forgets that the examples are essentially mathematical in nature. If you are an ecologist who has shied away from quantitative ecology in the past then this may be the text to convince you that there is much to be learnt from quantitative ecology. I thoroughly recommend this book and trust that you enjoy reading it as much as I did.” (International Statistical Review, 2012) "After a course of one or two semesters using this textbook, he says, students should have the absolute minimum of knowledge about quantitative research that ecologists need, but can provide a foundation for students who want to move further in that direction." (Book News, 1 August 2011) Table of ContentsHow I chose to write this book, and why you might choose to read it. Preface. 0. How to start a meaningful relationship with your computer. Introduction to R. 0.1 What is R? 0.2 Why use R for this book? 0.3 Computing with a scientific package like R. 0.4 Installing and interacting with R. 0.5 Style conventions. 0.6 Valuable R accessories. 0.7 Getting help. 0.8 Basic R usage. 0.9 Importing data from a spreadsheet. 0.10 Storing data in data frames. 0.11 Exporting data from R. 0.12 Quitting R. 1. How to make mathematical statements. Numbers, equations and functions. 1.1 Qualitative and quantitative scales. 1.2 Numbers. 1.3 Symbols. 1.4 Logical operations. 1.5 Algebraic operations. 1.6 Manipulating numbers. 1.7 Manipulating units. 1.8 Manipulating expressions. 1.9 Polynomials. 1.10 Equations. 1.11 First order polynomial equations. 1.12 Proportionality and scaling: a special kind of first order polynomial equation. 1.13 Second and higher order polynomial equations. 1.14 Systems of polynomial equations. 1.15 Inequalities. 1.16 Coordinate systems. 1.17 Complex numbers. 1.18 Relations and functions. 1.19 The graph of a function. 1.20 First order polynomial functions. 1.21 Higher order polynomial functions. 1.22 The relationship between equations and functions. 1.23 Other useful functions. 1.24 Inverse functions. 1.25 Functions of more than one variable. 2. How to describe regular shapes and patterns. Geometry and trigonometry. 2.1 Primitive elements. 2.2 Axioms of Euclidean geometry. 2.3 Propositions. 2.4 Distance between two points. 2.5 Areas and volumes. 2.6 Measuring angles. 2.7 The trigonometric circle. 2.8 Trigonometric functions. 2.9 Polar coordinates. 2.10 Graphs of trigonometric functions. 2.11 Trigonometric identities. 2.12 Inverses of trigonometric functions. 2.13 Trigonometric equations. 2.14 Modifying the basic trigonometric graphs. 2.15 Superimposing trigonometric functions. 2.16 Spectral analysis. 2.17 Fractal geometry. 3. How to change things, one step at a time. Sequences, difference equations and logarithms. 3.1 Sequences. 3.2 Difference equations. 3.3 Higher order difference equations. 3.4 Initial conditions and parameters. 3.5 Solutions of a difference equation. 3.6 Equilibrium solutions. 3.7 Stable and unstable equilibria. 3.8 Investigating stability. 3.9 Chaos. 3.10 Exponential function. 3.11 Logarithmic function. 3.12 Logarithmic equations. 4. How to change things, continuously. Derivatives and their applications. 4.1 Average rate of change. 4.2 Instantaneous rate of change. 4.3 Limits. 4.4 The derivative of a function. 4.5 Differentiating polynomials. 4.6 Differentiating other functions. 4.7 The chain rule. 4.8 Higher order derivatives. 4.9 Derivatives of functions of many variables. 4.10 Optimisation. 4.11 Local stability for difference equations. 4.12 Series expansions. 5. How to work with accumulated change. Integrals and their applications. 5.1 Antiderivatives. 5.2 Indefinite integrals. 5.3 Three analytical methods of integration. 5.4 Summation. 5.5 Area under a curve. 5.6 Definite integrals. 5.7 Some properties of definite integrals. 5.8 Improper integrals. 5.9 Differential equations. 5.10 Solving differential equations. 5.11 Stability analysis for differential equations. 6. How to keep stuff organised in tables. Matrices and their applications. 6.1 Matrices. 6.2 Matrix operations. 6.3 Geometric interpretation of vectors and square matrices. 6.4 Solving systems of equations with matrices. 6.5 Markov chains. 6.6 Eigenvalues and eigenvectors. 6.7 Leslie matrix models. 6.8 Analysis of linear dynamical systems. 6.9 Analysis of nonlinear dynamical systems. 7. How to visualise and summarise data. Descriptive statistics. 7.1 Overview of statistics. 7.2 Statistical variables. 7.3 Populations and samples. 7.4 Single-variable samples. 7.5 Frequency distributions. 7.6 Measures of centrality. 7.7 Measures of spread. 7.8 Skewness and kurtosis. 7.9 Graphical summaries. 7.10 Data sets with more than one variable. 7.11 Association between qualitative variables. 7.12 Association between quantitative variables. 7.13 Joint frequency distributions. 8. How to put a value on uncertainty. Probability. 8.1 Random experiments and event spaces. 8.2 Events. 8.3 Frequentist probability. 8.4 Equally likely events. 8.5 The union of events. 8.6 Conditional probability. 8.7 Independent events. 8.8 Total probability. 8.9 Bayesian probability. 9. How to identify different kinds of randomness. Probability distributions. 9.1 Probability distributions. 9.2 Discrete probability distributions. 9.3 Continuous probability distributions. 9.4 Expectation. 9.5 Named distributions. 9.6 Equally likely events: the uniform distribution. 9.7 Hit or miss: the Bernoulli distribution. 9.8 Count of occurrences in a given number of trials: the binomial distribution. 9.9 Counting different types of occurrences: the multinomial distribution. 9.10 Number of occurrences in a unit of time or space: the Poisson distribution. 9.11 The gentle art of waiting: geometric, negative binomial, exponential and gamma distributions. 9.12 Assigning probabilities to probabilities: the beta and Dirichlet distributions. 9.13 Perfect symmetry: the normal distribution. 9.14 Because it looks right: using probability distributions empirically. 9.15 Mixtures, outliers and the t-distribution. 9.16 Joint, conditional and marginal probability distributions. 9.17 The bivariate normal distribution. 9.18 Sums of random variables: the central limit theorem. 9.19 Products of random variables: the log-normal distribution. 9.20 Modelling residuals: the chi-square distribution. 9.21 Stochastic simulation. 10. How to see the forest from the trees. Estimation and testing. 10.1 Estimators and their properties. 10.2 Normal theory. 10.3 Estimating the population mean. 10.4 Estimating the variance of a normal population. 10.5 Confidence intervals. 10.6 Inference by bootstrapping. 10.7 More general estimation methods. 10.8 Estimation by least squares. 10.9 Estimation by maximum likelihood. 10.10 Bayesian estimation. 10.11 Link between maximum likelihood and Bayesian estimation. 10.12 Hypothesis testing: rationale. 10.13 Tests for the population mean. 10.14 Tests comparing two different means. 10.15 Hypotheses about qualitative data. 10.16 Hypothesis testing debunked. 11. How to separate the signal from the noise. Statistical modelling. 11.1 Comparing the means of several populations. 11.2 Simple linear regression. 11.3 Prediction. 11.4 How good is the best-fit line? 11.5 Multiple linear regression. 11.6 Model selection. 11.7 Generalised linear models. 11.8 Evaluation, diagnostics and model selection for GLMs. 11.9 Modelling dispersion. 11.10 Fitting more complicated models to data: polynomials, interactions, nonlinear regression. 11.11 Letting the data suggest more complicated models: smoothing. 11.12 Partitioning variation: mixed effects models. 12. How to measure similarity. Multivariate methods 12.1 The problem with multivariate data. 12.2 Ordination in general. 12.3 Principal components analysis. 12.4 Clustering in general. 12.5 Agglomerative hierarchical clustering. 12.6 Nonhierarchical clustering: k means analysis. 12.7 Classification in general. 12.8 Logistic regression: two classes. 12.9 Logistic regression: many classes. Further reading. References. Appendix: Formulae. R Index. Index.

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Book SynopsisHow to Be a Quantitative Ecologist is comprised of two equal parts on mathematics and statistics with emphasis on quantitative skills. A major component of this guide is computer implementation techniques, accompanied by computer practicals using the language R.Trade Review“For those looking through R books for something a bit more technical, this book will be an essential accomplice to mastering R.” (British Ecological Society, 1 April 2013) “The book is written in a style that is easy to read and for which one quickly forgets that the examples are essentially mathematical in nature. If you are an ecologist who has shied away from quantitative ecology in the past then this may be the text to convince you that there is much to be learnt from quantitative ecology. I thoroughly recommend this book and trust that you enjoy reading it as much as I did.” (International Statistical Review, 2012) "After a course of one or two semesters using this textbook, he says, students should have the absolute minimum of knowledge about quantitative research that ecologists need, but can provide a foundation for students who want to move further in that direction." (Book News, 1 August 2011) Table of ContentsHow I chose to write this book, and why you might choose to read it. Preface. 0. How to start a meaningful relationship with your computer. Introduction to R. 0.1 What is R? 0.2 Why use R for this book? 0.3 Computing with a scientific package like R. 0.4 Installing and interacting with R. 0.5 Style conventions. 0.6 Valuable R accessories. 0.7 Getting help. 0.8 Basic R usage. 0.9 Importing data from a spreadsheet. 0.10 Storing data in data frames. 0.11 Exporting data from R. 0.12 Quitting R. 1. How to make mathematical statements. Numbers, equations and functions. 1.1 Qualitative and quantitative scales. 1.2 Numbers. 1.3 Symbols. 1.4 Logical operations. 1.5 Algebraic operations. 1.6 Manipulating numbers. 1.7 Manipulating units. 1.8 Manipulating expressions. 1.9 Polynomials. 1.10 Equations. 1.11 First order polynomial equations. 1.12 Proportionality and scaling: a special kind of first order polynomial equation. 1.13 Second and higher order polynomial equations. 1.14 Systems of polynomial equations. 1.15 Inequalities. 1.16 Coordinate systems. 1.17 Complex numbers. 1.18 Relations and functions. 1.19 The graph of a function. 1.20 First order polynomial functions. 1.21 Higher order polynomial functions. 1.22 The relationship between equations and functions. 1.23 Other useful functions. 1.24 Inverse functions. 1.25 Functions of more than one variable. 2. How to describe regular shapes and patterns. Geometry and trigonometry. 2.1 Primitive elements. 2.2 Axioms of Euclidean geometry. 2.3 Propositions. 2.4 Distance between two points. 2.5 Areas and volumes. 2.6 Measuring angles. 2.7 The trigonometric circle. 2.8 Trigonometric functions. 2.9 Polar coordinates. 2.10 Graphs of trigonometric functions. 2.11 Trigonometric identities. 2.12 Inverses of trigonometric functions. 2.13 Trigonometric equations. 2.14 Modifying the basic trigonometric graphs. 2.15 Superimposing trigonometric functions. 2.16 Spectral analysis. 2.17 Fractal geometry. 3. How to change things, one step at a time. Sequences, difference equations and logarithms. 3.1 Sequences. 3.2 Difference equations. 3.3 Higher order difference equations. 3.4 Initial conditions and parameters. 3.5 Solutions of a difference equation. 3.6 Equilibrium solutions. 3.7 Stable and unstable equilibria. 3.8 Investigating stability. 3.9 Chaos. 3.10 Exponential function. 3.11 Logarithmic function. 3.12 Logarithmic equations. 4. How to change things, continuously. Derivatives and their applications. 4.1 Average rate of change. 4.2 Instantaneous rate of change. 4.3 Limits. 4.4 The derivative of a function. 4.5 Differentiating polynomials. 4.6 Differentiating other functions. 4.7 The chain rule. 4.8 Higher order derivatives. 4.9 Derivatives of functions of many variables. 4.10 Optimisation. 4.11 Local stability for difference equations. 4.12 Series expansions. 5. How to work with accumulated change. Integrals and their applications. 5.1 Antiderivatives. 5.2 Indefinite integrals. 5.3 Three analytical methods of integration. 5.4 Summation. 5.5 Area under a curve. 5.6 Definite integrals. 5.7 Some properties of definite integrals. 5.8 Improper integrals. 5.9 Differential equations. 5.10 Solving differential equations. 5.11 Stability analysis for differential equations. 6. How to keep stuff organised in tables. Matrices and their applications. 6.1 Matrices. 6.2 Matrix operations. 6.3 Geometric interpretation of vectors and square matrices. 6.4 Solving systems of equations with matrices. 6.5 Markov chains. 6.6 Eigenvalues and eigenvectors. 6.7 Leslie matrix models. 6.8 Analysis of linear dynamical systems. 6.9 Analysis of nonlinear dynamical systems. 7. How to visualise and summarise data. Descriptive statistics. 7.1 Overview of statistics. 7.2 Statistical variables. 7.3 Populations and samples. 7.4 Single-variable samples. 7.5 Frequency distributions. 7.6 Measures of centrality. 7.7 Measures of spread. 7.8 Skewness and kurtosis. 7.9 Graphical summaries. 7.10 Data sets with more than one variable. 7.11 Association between qualitative variables. 7.12 Association between quantitative variables. 7.13 Joint frequency distributions. 8. How to put a value on uncertainty. Probability. 8.1 Random experiments and event spaces. 8.2 Events. 8.3 Frequentist probability. 8.4 Equally likely events. 8.5 The union of events. 8.6 Conditional probability. 8.7 Independent events. 8.8 Total probability. 8.9 Bayesian probability. 9. How to identify different kinds of randomness. Probability distributions. 9.1 Probability distributions 300 9.2 Discrete probability distributions 301 9.3 Continuous probability distributions 304 9.4 Expectation 306 9.5 Named distributions 309 9.6 Equally likely events: the uniform distribution. 9.7 Hit or miss: the Bernoulli distribution. 9.8 Count of occurrences in a given number of trials: the binomial distribution. 9.9 Counting different types of occurrences: the multinomial distribution. 9.10 Number of occurrences in a unit of time or space: the Poisson distribution. 9.11 The gentle art of waiting: geometric, negative binomial, exponential and gamma distributions. 9.12 Assigning probabilities to probabilities: the beta and Dirichlet distributions. 9.13 Perfect symmetry: the normal distribution. 9.14 Because it looks right: using probability distributions empirically. 9.15 Mixtures, outliers and the t-distribution. 9.16 Joint, conditional and marginal probability distributions. 9.17 The bivariate normal distribution. 9.18 Sums of random variables: the central limit theorem. 9.19 Products of random variables: the log-normal distribution. 9.20 Modelling residuals: the chi-square distribution. 9.21 Stochastic simulation. 10. How to see the forest from the trees. Estimation and testing. 10.1 Estimators and their properties. 10.2 Normal theory. 10.3 Estimating the population mean. 10.4 Estimating the variance of a normal population. 10.5 Confidence intervals. 10.6 Inference by bootstrapping. 10.7 More general estimation methods. 10.8 Estimation by least squares. 10.9 Estimation by maximum likelihood. 10.10 Bayesian estimation. 10.11 Link between maximum likelihood and Bayesian estimation. 10.12 Hypothesis testing: rationale. 10.13 Tests for the population mean. 10.14 Tests comparing two different means. 10.15 Hypotheses about qualitative data. 10.16 Hypothesis testing debunked. 11. How to separate the signal from the noise. Statistical modelling. 11.1 Comparing the means of several populations. 11.2 Simple linear regression. 11.3 Prediction. 11.4 How good is the best-fit line? 11.5 Multiple linear regression. 11.6 Model selection. 11.7 Generalised linear models. 11.8 Evaluation, diagnostics and model selection for GLMs. 11.9 Modelling dispersion 409 11.10 Fitting more complicated models to data: polynomials, interactions, nonlinear regression. 11.11 Letting the data suggest more complicated models: smoothing. 11.12 Partitioning variation: mixed effects models. 12. How to measure similarity. Multivariate methods 12.1 The problem with multivariate data. 12.2 Ordination in general. 12.3 Principal components analysis. 12.4 Clustering in general. 12.5 Agglomerative hierarchical clustering. 12.6 Nonhierarchical clustering: k means analysis. 12.7 Classification in general. 12.8 Logistic regression: two classes. 12.9 Logistic regression: many classes. Further reading. References. Appendix: Formulae. R Index. Index.

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Book SynopsisIt is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions.Table of ContentsPreface xvii List of Contributors xix Part I Introduction 1 1 A Short History of Compositional Data Analysis 3 John Bacon-Shone 1.1 Introduction 3 1.2 Spurious Correlation 3 1.3 Log and Log-Ratio Transforms 4 1.4 Subcompositional Dependence 5 1.5 alr, clr, ilr: Which Transformation to Choose? 5 1.6 Principles, Perturbations and Back to the Simplex 6 1.7 Biplots and Singular Value Decompositions 7 1.8 Mixtures 7 1.9 Discrete Compositions 8 1.10 Compositional Processes 8 1.11 Structural, Counting and Rounded Zeros 8 1.12 Conclusion 9 Acknowledgement 9 References 9 2 Basic Concepts and Procedures 12 Juan Jos´e Egozcue and Vera Pawlowsky-Glahn 2.1 Introduction 12 2.2 Election Data and Raw Analysis 13 2.3 The Compositional Alternative 15 2.3.1 Scale Invariance: Vectors with Proportional Positive Components Represent the Same Composition 15 2.3.2 Subcompositional Coherence: Analyses Concerning a Subset of Parts Must Not Depend on Other Non-Involved Parts 16 2.3.3 Permutation Invariance: The Conclusions of a Compositional Analysis Should Not Depend on the Order of the Parts 17 2.4 Geometric Settings 17 2.5 Centre and Variability 22 2.6 Conclusion 27 Acknowledgements 27 References 27 Part II Theory – Statistical Modelling 29 3 The Principle of Working on Coordinates 31 Glòria Mateu-Figueras, Vera Pawlowsky-Glahn and Juan José Egozcue 3.1 Introduction 31 3.2 The Role of Coordinates in Statistics 32 3.3 The Simplex 33 3.3.1 Basis of the Simplex 34 3.3.2 Working on Orthonormal Coordinates 35 3.4 Move or Stay in the Simplex 38 3.5 Conclusions 40 Acknowledgements 41 References 41 4 Dealing with Zeros 43 Josep Antoni Martún-Fernández, Javier Palarea-Albaladejo and Ricardo Antonio Olea 4.1 Introduction 43 4.2 Rounded Zeros 44 4.2.1 Non-Parametric Replacement of Rounded Zeros 45 4.2.2 Parametric Modified EM Algorithm for Rounded Zeros 47 4.3 Count Zeros 50 4.4 Essential Zeros 53 4.5 Difficulties, Troubles and Challenges 55 Acknowledgements 57 References 57 5 Robust Statistical Analysis 59 Peter Filzmoser and Karel Hron 5.1 Introduction 59 5.2 Elements of Robust Statistics from a Compositional Point of View 60 5.3 Robust Methods for Compositional Data 63 5.3.1 Multivariate Outlier Detection 64 5.3.2 Principal Component Analysis 64 5.3.3 Discriminant Analysis 65 5.4 Case Studies 66 5.4.1 Multivariate Outlier Detection 66 5.4.2 Principal Component Analysis 68 5.4.3 Discriminant Analysis 68 5.5 Summary 70 Acknowledgement 71 References 71 6 Geostatistics for Compositions 73 Raimon Tolosana-Delgado, Karl Gerald van den Boogaart and Vera Pawlowsky-Glahn 6.1 Introduction 73 6.2 A Brief Summary of Geostatistics 74 6.3 Cokriging of Regionalised Compositions 76 6.4 Structural Analysis of Regionalised Composition 76 6.5 Dealing with Zeros: Replacement Strategies and Simplicial Indicator Cokriging 78 6.6 Application 79 6.6.1 Delimiting the Body: Simplicial Indicator Kriging 81 6.6.2 Interpolating the Oil–Brine–Solid Content 82 6.7 Conclusions 84 Acknowledgements 84 References 84 7 Compositional VARIMA Time Series 87 Carles Barceló-Vidal, Lucúa Aguilar and Josep Antoni Martún-Fernández 7.1 Introduction 87 7.2 The Simplex SD as a Compositional Space 89 7.2.1 Basic Concepts and Notation 89 7.2.2 The Covariance Structure on the Simplex 90 7.3 Compositional Time Series Models 91 7.3.1 C-Stationary Processes 92 7.3.2 C-VARIMA Processes 93 7.4 CTS Modelling: An Example 94 7.4.1 Expenditure Shares in the UK 94 7.4.2 Model Selection 95 7.4.3 Estimation of Parameters 96 7.4.4 Interpretation and Comparison 96 7.5 Discussion 99 Acknowledgements 99 References 100 Appendix 102 8 Compositional Data and Correspondence Analysis 104 Michael Greenacre 8.1 Introduction 104 8.2 Comparative Technical Definitions 105 8.3 Properties and Interpretation of LRA and CA 107 8.4 Application to Fatty Acid Compositional Data 107 8.5 Discussion and Conclusions 111 Acknowledgements 112 References 112 9 Use of Survey Weights for the Analysis of Compositional Data 114 Monique Graf 9.1 Introduction 114 9.2 Elements of Survey Design 115 9.2.1 Randomization 115 9.2.2 Design-Based Estimation 118 9.3 Application to Compositional Data 122 9.3.1 Weighted Arithmetic and Geometric Means 123 9.3.2 Closed Arithmetic Mean of Amounts 123 9.3.3 Centred Log-Ratio of the Geometric Mean Composition 124 9.3.4 Closed Geometric Mean Composition 124 9.3.5 Example: Swiss Earnings Structure Survey (SESS) 125 9.4 Discussion 126 References 126 10 Notes on the Scaled Dirichlet Distribution 128 Gianna Serafina Monti, Glòria Mateu-Figueras and Vera Pawlowsky-Glahn 10.1 Introduction 128 10.2 Genesis of the Scaled Dirichlet Distribution 129 10.3 Properties of the Scaled Dirichlet Distribution 131 10.3.1 Graphical Comparison 131 10.3.2 Membership in the Exponential Family 133 10.3.3 Measures of Location and Variability 134 10.4 Conclusions 136 Acknowledgements 137 References 137 Part III Theory – Algebra and Calculus 139 11 Elements of Simplicial Linear Algebra and Geometry 141 Juan José Egozcue, Carles Barceló-Vidal, Josep Antoni Martún-Fernández, Eusebi Jarauta-Bragulat, José Luis Dúaz-Barrero and Glòria Mateu-Figueras 11.1 Introduction 141 11.2 Elements of Simplicial Geometry 142 11.2.1 n-Part Simplex 142 11.2.2 Vector Space 143 11.2.3 Centred Log-Ratio Representation 146 11.2.4 Metrics 147 11.2.5 Orthonormal Basis and Coordinates 149 11.3 Linear Functions 151 11.3.1 Linear Functions Defined on the Simplex 152 11.3.2 Simplicial Linear Function Defined on a Real Space 153 11.3.3 Simplicial Linear Function Defined on the Simplex 154 11.4 Conclusions 156 Acknowledgements 156 References 156 12 Calculus of Simplex-Valued Functions 158 Juan José Egozcue, Eusebi Jarauta-Bragulat and José Luis Díaz-Barrero 12.1 Introduction 158 12.2 Limits, Continuity and Differentiability 161 12.2.1 Limits and Continuity 161 12.2.2 Differentiability 163 12.2.3 Higher Order Derivatives 169 12.3 Integration 171 12.3.1 Antiderivatives. Indefinite Integral 171 12.3.2 Integration of Continuous SV Functions 172 12.4 Conclusions 174 Acknowledgements 175 References 175 13 Compositional Differential Calculus on the Simplex 176 Carles Barceló-Vidal, Josep Antoni Martún-Fernández and Glòria Mateu-Figueras 13.1 Introduction 176 13.2 Vector-Valued Functions on the Simplex 177 13.2.1 Scale-Invariant Vector-Valued Functions on Rn + 177 13.2.2 Vector-Valued Functions on Sn 178 13.3 C-Derivatives on the Simplex 178 13.3.1 Derivative of a Scale-Invariant Vector-Valued Function on Rn + 178 13.3.2 Directional C-Derivatives 180 13.3.3 C-Derivative 182 13.3.4 C-Gradient 184 13.3.5 Critical Points of a C-Differentiable Real-Valued Function on Sn 184 13.4 Example: Experiments with Mixtures 185 13.4.1 Polynomial of Degree One 185 13.4.2 Polynomial of Degree Two 186 13.4.3 Polynomial of Degree One in Logarithms 187 13.4.4 A numerical Example 188 13.5 Discussion 189 Acknowledgements 190 References 190 Part IV Applications 191 14 Proportions, Percentages, PPM: Do the Molecular Biosciences Treat Compositional Data Right? 193 David Lovell, Warren Müller, Jen Taylor, Alec Zwart and Chris Helliwell 14.1 Introduction 193 14.2 The Omics Imp and Two Bioscience Experiment Paradigms 194 14.3 The Impact of Compositional Constraints in the Omics 197 14.3.1 Univariate Impact of Compositional Constraints 197 14.3.2 Impact of Compositional Constraints on Multivariate Distance Metrics 199 14.4 Impact of Compositional Constraints on Correlation and Covariance 201 14.4.1 Compositional Constraints, Covariance, Correlation and Log-Transformed Data 202 14.4.2 A Simulation Approach to Understanding the Impact of Closure 202 14.5 Implications 204 14.5.1 Gathering Information to Infer Absolute Abundance 204 14.5.2 Analysing Compositional Omics Data Appropriately 205 Acknowledgements 206 References 206 15 Hardy–Weinberg Equilibrium: A Nonparametric Compositional Approach 208 Jan Graffelman and Juan José Egozcue 15.1 Introduction 208 15.2 Genetic Data Sets 209 15.3 Classical Tests for HWE 210 15.4 A Compositional Approach 210 15.5 Example 214 15.6 Conclusion and Discussion 215 Acknowledgements 215 References 215 16 Compositional Analysis in Behavioural and Evolutionary Ecology 218 Michele Edoardo Raffaele Pierotti and Josep Antoni Martún-Fernández 16.1 Introduction 218 16.2 CODA in Population Genetics 219 16.3 CODA in Habitat Choice 222 16.4 Multiple Choice and Individual Variation in Preferences 224 16.5 Ecological Specialization 228 16.6 Time Budgets: More on Specialization 229 16.7 Conclusions 231 Acknowledgements 231 References 231 17 Flying in Compositional Morphospaces: Evolution of Limb Proportions in Flying Vertebrates 235 Luis Azevedo Rodrigues, Josep Daunis-i-Estadella, Glòria Mateu-Figueras and Santiago Thi´o-Henestrosa 17.1 Introduction 235 17.2 Flying Vertebrates – General Anatomical and Functional Characteristics 236 17.3 Materials 236 17.4 Methods 238 17.5 Aitchison Distance Disparity Metrics 239 17.5.1 Intragroup Aitchison Distance 239 17.5.2 Intergroup Aitchison Distance 240 17.6 Statistical Tests 243 17.7 Biplots 244 17.7.1 Chiroptera 244 17.7.2 Pterosauria 245 17.8 Balances 246 17.9 Size Effect 249 17.10 Final Remarks 249 17.10.1 All Groups 250 17.10.2 Aves 250 17.10.3 Pterosauria 250 17.10.4 Chiroptera 251 Acknowledgements 252 References 252 18 Natural Laws Governing the Distribution of the Elements in Geochemistry: The Role of the Log-Ratio Approach 255 Antonella Buccianti 18.1 Introduction 255 18.2 Geochemical Processes and Log-Ratio Approach 256 18.3 Log-Ratio Approach and Water Chemistry 258 18.4 Log-Ratio Approach and Volcanic Gas Chemistry 261 18.5 Log-Ratio Approach and Subducting Sediment Composition 263 18.6 Conclusions 265 Acknowledgements 265 References 265 19 Compositional Data Analysis in Planetology: The Surfaces of Mars and Mercury 267 Helmut Lammer, Peter Wurz, Josep Antoni Martún-Fernández and Herbert Iwo Maria Lichtenegger 19.1 Introduction 267 19.1.1 Mars 267 19.1.2 Mercury 269 19.1.3 Analysis of Surface Composition 270 19.2 Compositional Analysis of Mars’ Surface 270 19.3 Compositional Analysis of Mercury’s Surface 274 19.4 Conclusion 278 Acknowledgement 278 References 278 20 Spectral Analysis of Compositional Data in Cyclostratigraphy 282 Eulogio Pardo-Igúzquiza and Javier Heredia 20.1 Introduction 282 20.2 The Method 283 20.3 Case Study 285 20.4 Discussion 287 20.5 Conclusions 288 Acknowledgement 288 References 288 21 Multivariate Geochemical Data Analysis in Physical Geography 290 Jennifer McKinley and Christopher David Lloyd 21.1 Introduction 290 21.2 Context 291 21.3 Data 293 21.4 Analysis 295 21.5 Discussion 299 21.6 Conclusion 300 Acknowledgement 300 References 300 22 Combining Isotopic and Compositional Data: A Discrimination of Regions Prone to Nitrate Pollution 302 Roger Puig, Raimon Tolosana-Delgado, Neus Otero and Albert Folch 22.1 Introduction 302 22.2 Study Area 303 22.2.1 Maresme 304 22.2.2 Osona 305 22.2.3 Lluc¸an`es 305 22.2.4 Empord`a 306 22.2.5 Selva 306 22.3 Analytical Methods 306 22.4 Statistical Treatment 307 22.4.1 Data Scaling 307 22.4.2 Linear Discriminant Analysis 309 22.4.3 Discriminant Biplots 310 22.5 Results and Discussion 311 22.6 Conclusions 314 Acknowledgements 315 References 315 23 Applications in Economics 318 Tim Fry 23.1 Introduction 318 23.2 Consumer Demand Systems 319 23.3 Miscellaneous Applications 322 23.4 Compositional Time Series 323 23.5 New Directions 323 23.6 Conclusion 325 References 325 Part V Software 327 24 Exploratory Analysis Using CoDaPack 3D 329 Santiago Thió-Henestrosa and Josep Daunis-i-Estadella 24.1 CoDaPack 3D Description 329 24.2 Data Set Description 331 24.3 Exploratory Analysis 333 24.3.1 Numerical Analysis 333 24.3.2 Biplot 334 24.3.3 The Ternary Diagram 335 24.3.4 Principal Component Analysis 336 24.3.5 Balance-Dendrogram 336 24.3.6 By Groups Description 338 24.4 Summary and Conclusions 339 Acknowledgements 340 References 340 25 robCompositions: An R-package for Robust Statistical Analysis of Compositional Data 341 Matthias Templ, Karel Hron and Peter Filzmoser 25.1 General Information on the R-package robCompositions 341 25.1.1 Data Sets Included in the Package 342 25.1.2 Design Principles 343 25.2 Expressing Compositional Data in Coordinates 343 25.3 Multivariate Statistical Methods for Compositional Data Containing Outliers 345 25.3.1 Multivariate Outlier Detection 345 25.3.2 Principal Component Analysis and the Robust Compositional Biplot 347 25.3.3 Discriminant Analysis 350 25.4 Robust Imputation of Missing Values 351 25.5 Summary 354 References 354 26 Linear Models with Compositions in R 356 Raimon Tolosana-Delgado and Karl Gerald van den Boogaart 26.1 Introduction 356 26.2 The Illustration Data Set 357 26.2.1 The Data 357 26.2.2 Descriptive Analysis of Compositional Characteristics 358 26.3 Explanatory Binary Variable 360 26.4 Explanatory Categorical Variable 363 26.5 Explanatory Continuous Variable 365 26.6 Explanatory Composition 367 26.7 Conclusions 370 Acknowledgement 371 References 371 Index 373

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Book SynopsisBayesian networks have found application in a number of fields, including risk analysis, consumer help desks, tissue pathology, pattern recognition, credit assessment, computer network diagnosis, and artificial intelligence. Bayesian Networks is a self-contained introduction to the theory and applications of Bayesian networks.Trade Review"It assumes only a basic knowledge of probability, statistics and mathematics and is well suited for classroom teaching . . . Each chapter of the book is concluded with short notes on the literature and a set of helpful exercises." (Mathematical Reviews, 2011) "Extensively tested in classroom teaching … .The authors clearly define all concepts and provide numerous examples and exercises." (Book News, December 2009)Table of ContentsPreface. 1 Graphical models and probabilistic reasoning. 1.1 Introduction. 1.2 Axioms of probability and basic notations. 1.3 The Bayes update of probability. 1.4 Inductive learning. 1.5 Interpretations of probability and Bayesian networks. 1.6 Learning as inference about parameters. 1.7 Bayesian statistical inference. 1.8 Tossing a thumb-tack. 1.9 Multinomial sampling and the Dirichlet integral. Notes. Exercises: Probabilistic theories of causality, Bayes’ rule, multinomial sampling and the Dirichlet density. 2 Conditional independence, graphs and d-separation. 2.1 Joint probabilities. 2.2 Conditional independence. 2.3 Directed acyclic graphs and d-separation. 2.4 The Bayes ball. 2.5 Potentials. 2.6 Bayesian networks. 2.7 Object oriented Bayesian networks. 2.8 d-Separation and conditional independence. 2.9 Markov models and Bayesian networks. 2.10 I-maps and Markov equivalence. Notes. Exercises: Conditional independence and d-separation. 3 Evidence, sufficiency and Monte Carlo methods. 3.1 Hard evidence. 3.2 Soft evidence and virtual evidence. 3.3 Queries in probabilistic inference. 3.4 Bucket elimination. 3.5 Bayesian sufficient statistics and prediction sufficiency. 3.6 Time variables. 3.7 A brief introduction to Markov chain Monte Carlo methods. 3.8 The one-dimensional discrete Metropolis algorithm. Notes. Exercises: Evidence, sufficiency and Monte Carlo methods. 4 Decomposable graphs and chain graphs. 4.1 Definitions and notations. 4.2 Decomposable graphs and triangulation of graphs. 4.3 Junction trees. 4.4 Markov equivalence. 4.5 Markov equivalence, the essential graph and chain graphs. Notes. Exercises: Decomposable graphs and chain graphs. 5 Learning the conditional probability potentials. 5.1 Initial illustration: maximum likelihood estimate for a fork connection. 5.2 The maximum likelihood estimator for multinomial sampling. 5.3 MLE for the parameters in a DAG: the general setting. 5.4 Updating, missing data, fractional updating. Notes. Exercises: Learning the conditional probability potentials. 6 Learning the graph structure. 6.1 Assigning a probability distribution to the graph structure. 6.2 Markov equivalence and consistency. 6.3 Reducing the size of the search. 6.4 Monte Carlo methods for locating the graph structure. 6.5 Women in mathematics. Notes. Exercises: Learning the graph structure. 7 Parameters and sensitivity. 7.1 Changing parameters in a network. 7.2 Measures of divergence between probability distributions. 7.3 The Chan-Darwiche distance measure. 7.4 Parameter changes to satisfy query constraints. 7.5 The sensitivity of queries to parameter changes. Notes. Exercises: Parameters and sensitivity. 8 Graphical models and exponential families. 8.1 Introduction to exponential families. 8.2 Standard examples of exponential families. 8.3 Graphical models and exponential families. 8.4 Noisy ‘or’ as an exponential family. 8.5 Properties of the log partition function. 8.6 Fenchel Legendre conjugate. 8.7 Kullback-Leibler divergence. 8.8 Mean field theory. 8.9 Conditional Gaussian distributions. Notes. Exercises: Graphical models and exponential families. 9 Causality and intervention calculus. 9.1 Introduction. 9.2 Conditioning by observation and by intervention. 9.3 The intervention calculus for a Bayesian network. 9.4 Properties of intervention calculus. 9.5 Transformations of probability. 9.6 A note on the order of ‘see’ and ‘do’ conditioning. 9.7 The ‘Sure Thing’ principle. 9.8 Back door criterion, confounding and identifiability. Notes. Exercises: Causality and intervention calculus. 10 The junction tree and probability updating. 10.1 Probability updating using a junction tree. 10.2 Potentials and the distributive law. 10.3 Elimination and domain graphs. 10.4 Factorization along an undirected graph. 10.5 Factorizing along a junction tree. 10.6 Local computation on junction trees. 10.7 Schedules. 10.8 Local and global consistency. 10.9 Message passing for conditional Gaussian distributions. 10.10 Using a junction tree with virtual evidence and soft evidence. Notes. Exercises: The junction tree and probability updating. 11 Factor graphs and the sum product algorithm. 11.1 Factorization and local potentials. 11.2 The sum product algorithm. 11.3 Detailed illustration of the algorithm. Notes. Exercise: Factor graphs and the sum product algorithm. References. Index.

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Book Synopsis- It reveals the interrelationships between multiple variables and features of the underlying conditional independence. - It covers conditional independence, several types of independence graphs, Gaussian models, issues in model selection, regression and decomposition. - Many numerical examples and exercises with solutions are included.Table of ContentsIndependence and Interaction. Independence Graphs. Information Divergence. The Inverse Variance. Graphical Gaussian Models. Graphical Log-Linear Models. Model Selection. Methods for Sparse Tables. Regression and Graphical Chain Models. Models for Mixed Variables. Decompositions and Decomposability. Appendices. References. Author Index. Subject Index.

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Book SynopsisThis practical text is an essential source of information for those wanting to know how to deal with the variability that exists in every engineering situation. Using typical engineering data, it presents the basic statistical methods that are relevant, in simple numerical terms.Trade Review"This book appeals to students in all areas of engineering and also managers concerned with the quality of manufactured products. Academic engineers can use this text to teach their students basic practical skills in quality management and statistical engineering, without getting involved in the complex mathematical theory of probability on which statistical science is dependent." (Zentralblatt MATH, 1 August 2013) "This is a timely text that helps to support the development of these important skills. Its no-nonsense and useful approach gives a flavour of the main statistical tools and techniques in basic language." (Quality World, December 2009) "It deserves to become a standard text to encourage the best in industrial practice." (Engineering & Technology, November 2009)Table of ContentsAbout the Author vii Foreword ix Preface xi Acknowledgements xiii 1 Nature of Variability 1 2 Basic Statistical Methods 9 2.1 Variance 9 2.2 Divisor ‘n’ or ‘n-1’? 11 2.3 Covariance and Correlation 13 2.4 Normal Distribution 14 2.5 Cumulative Frequency Distributions 18 2.6 Binomial Distribution 20 2.7 Poisson Distribution 25 2.8 Chi-squared Distribution 26 Bibliography 31 3 Production 33 3.1 Sampling Inspection 34 3.2 Control Charts 37 3.3 Cusum Charts 40 3.4 Significance Tests 43 3.5 Analysis of Variance 49 3.6 Linear Regression 52 Bibliography 57 4 Engineering Design 61 4.1 Variance Synthesis 61 4.2 Factors of Safety 68 4.3 Tolerances 69 4.4 The Future 71 Bibliography 72 5 Research and Development 75 5.1 Design of Experiments 76 5.2 Evolutionary Operation 95 5.3 Multiple Regression 96 5.4 More Statistical Methods 111 Bibliography 115 6 Background 119 6.1 Measurement 119 6.2 Statistical Computing 121 Bibliography 127 7 Quality Management 129 7.1 Quality Planning 129 7.2 Quality Organisation 135 7.3 Directing the Quality Function 137 7.4 Controlling the Quality Function 140 7.5 Statistical Engineering 141 Bibliography 142 8 Conclusion 145 Appendix A: Guidelines 147 Appendix B: Recommended Books 151 Appendix C: Periodicals 161 Appendix D: Supplementary Bibliography 165 Appendix E: Statistical Tables 171 Index 173

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Book SynopsisThis book aims to get the electrical and electronic engineering student well-versed in the machinery of probability theory. It steers clear of getting into application areas any more than is needed to get the reader comfortable with the mathematics and connecting it to models of practical situations.Trade Review"After reading some introductory material on conventions and notions, it is possible to use separate chapters as introductions to various ideas. This is how readers should use this book." (Computing Reviews, 1 October 2011)Table of ContentsPreface. Introduction. Part I. The Basic Model. Part I Introduction. Section 1. Dealing with ‘Real-World’ Problems. Section 2. The Probabilistic Experiment. Section 3. Outcome. Section 4. Events. Section 5. The Connection to the Mathematical World. Section 6. Elements and Sets. Section 7. Classes of Sets. Section 8. Elementary Set Operations. Section 9. Additional Set Operations. Section 10. Functions. Section 11. The Size of a Set. Section 12. Multiple and Infinite Set Operations. Section 13. More About Additive Classes. Section 14. Additive Set Functions. Section 15. More about Probabilistic Experiments. Section 16. The Probability Function. Section 17. Probability Space. Section 18. Simple Probability Arithmetic. Part I Summary. Part II. The Approach to Elementary Probability Problems. Part II. Introduction. Section 19. About Probability Problems. Section 20. Equally Likely Possible Outcomes. Section 21. Conditional Probability. Section 22. Conditional Probability Distributions. Section 23. Independent Events. Section 24. Classes of Independent Events. Section 25. Possible Outcomes Represented as Ordered k-Tuples. Section 26. Product Experiments and Product Spaces. Section 27. Product Probability Spaces. Section 28. Dependence Between the Components in an Ordered k-Tuple. Section 29. Multiple Observations Without Regard to Order. Section 30. Unordered Sampling with Replacement. Section 31. More Complicated Discrete Probability Problems. Section 32. Uncertainty and Randomness. Section 33. Fuzziness. Part II Summary. Part III. Introduction to Random Variables. Part III. Introduction. Section 34. Numerical-Valued Outcomes. Section 35. The Binomial Distribution. Section 36. The Real Numbers. Section 37. General Definition of a Random Variable. Section 38. The Cumulative Distribution Function. Section 39. The Probability Density Function. Section 40. The Gaussian Distribution. Section 41. Two Discrete Random Variables. Section 42. Two Arbitrary Random Variables. Section 43. Two-Dimensional Distribution Functions. Section 44. Two-Dimensional Density Functions. Section 45. Two Statistically Independent Random Variables. Section 46. Two Statistically Independent Random Variables-Absolutely Continuous Case. Part III Summary. Part IV. Transformations and Multiple Random Variables. Part IV Introduction. Section 47. Transformation of a Random Variable. Section 48. Transformation of a Two-Dimensional Random Variable. Section 49. The Sum of Two Discrete Random Variables. Section 50. The Sum of Two Arbitrary Random Variables. Section 51. n-Dimensional Random Variables. Section 52. Absolutely Continuous n-Dimensional R. V.’s. Section 53. Coordinate Transformations. Section 54. Rotations and the Bivariate Gaussian Distribution. Section 55. Several Statistically Independent Random Variables. Section 56. Singular Distributions in One Dimension. Section 57. Conditional Induced Distribution, Given an Event. Section 58. Resolving a Distribution into Components of Pure Type. Section 59. Conditional Distribution Given the Value of a Random Variable. Section 60. Random Occurrences in Time. Part IV Summary. Part V. Parameters for Describing Random Variables and Induced Distributions. Section 61. Some Properties of a Random Variable. Section 62. Higher Moments. Section 63. Expectation of a Function of a Random Variable. Section 64. The Variance of a Function of a Random Variable. Section 65. Bounds on the Induced Distribution. Section 66. Test Sampling. Section 67. Conditional Expectation with Respect to an Event. Section 68. Covariance and Correlation Coefficient. Section 69. The Correlation Coefficient as Parameter in a Joint Distribution. Section 70. More General Kinds of Dependence Between Random Variables. Section 71. The Covariance Matrix. Section 72. Random Variables as the Elements of a Vector Space. Section 73. Estimation. Section 74. The Stieltjes Integral. Part V Summary. Part VI. Further Topics in Random Variables. Part VI Introduction. Section 75. Complex Random Variables. Section 76. The Characteristic Function. Section 77. Characteristic Function of a Transformed Random Variable. Section 78. Characteristic Function of a Multidimensional Random Variable. Section 79. The Generating Function. Section 80. Several Jointly Gaussian Random Variables. Section 81. Spherically Symmetric Vector Random Variables. Section 82. Entropy Associated with Random Variables. Section 83. Copulas. Section 84. Sequences of Random Variables. Section 85. Convergent Sequences and Laws of Large Numbers. Section 86. Convergence of Probability Distributions and the Central Limit Theorem. Part VI Summary. Appendices. Notation and Abbreviations. References. Subject Index.

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Book SynopsisThroughout the social, medical and other sciences the importance of understanding complex hierarchical data structures is well understood. Multilevel modelling is now the accepted statistical technique for handling such data and is widely available in computer software packages. A thorough understanding of these techniques is therefore important for all those working in these areas. This new edition of Multilevel Statistical Models brings these techniques together, starting from basic ideas and illustrating how more complex models are derived. Bayesian methodology using MCMC has been extended along with new material on smoothing models, multivariate responses, missing data, latent normal transformations for discrete responses, structural equation modeling and survival models. Key Features: Provides a clear introduction and a comprehensive account of multilevel models. New methodological developments and applications are explored. Written by a leading Trade Review"This book is suitable as a comprehensive text for postgraduate courses, as well as a general reference guide. Applied statisticians in the social sciences, economics, biological and medical disciplines will find this book beneficial. See the review of the third edition." (Zentralblatt MATH, 1 December 2013) "This book would also serve as an outstanding general reference on multilevel models, since it offers concise and easy to follow descriptions of the various multilevel models and their applications, in addition to the references on which this work is based. I really enjoyed reading this book, and am sure that others will have a similar pleasurable experience." (Journal of Biopharmaceutical Statistics (JBS), 2012) Table of ContentsContents Dedication Preface Acknowledgements Notation A general classification notation and diagram Glossary Chapter 1 An introduction to multilevel models 1.1 Hierarchically structured data 1.2 School effectiveness 1.3 Sample survey methods 1.4 Repeated measures data 1.5 Event history and survival models 1.6 Discrete response data 1.7 Multivariate models 1.8 Nonlinear models 1.9 Measurement errors 1.10 Cross classifications and multiple membership structures. 1.11 Factor analysis and structural equation models 1.12 Levels of aggregation and ecological fallacies 1.13 Causality 1.14 The latent normal transformation and missing data 1.15 Other texts 1.16 A caveat Chapter 2 The 2-level model 2.1 Introduction 2.2 The 2-level model 2.3 Parameter estimation 2.4 Maximum likelihood estimation using Iterative Generalised Least Squares (IGLS) 2.5 Marginal models and Generalized Estimating Equations (GEE) 2.6 Residuals 2.7 The adequacy of Ordinary Least Squares estimates. 2.8 A 2-level example using longitudinal educational achievement data 2.9 General model diagnostics 2.10 Higher level explanatory variables and compositional effects 2.11 Transforming to normality 2.12 Hypothesis testing and confidence intervals 2.13 Bayesian estimation using Markov Chain Monte Carlo (MCMC) 2.14 Data augmentation Appendix 2.1 The general structure and maximum likelihood estimation for a multilevel model Appendix 2.2 Multilevel residuals estimation Appendix 2.3 Estimation using profile and extended likelihood Appendix 2.4 The EM algorithm Appendix 2.5 MCMC sampling Chapter 3. Three level models and more complex hierarchical structures. 3.1 Complex variance structures 3.2 A 3-level complex variation model example. 3.3 Parameter Constraints 3.4 Weighting units 3.5 Robust (Sandwich) Estimators and Jacknifing 3.6 The bootstrap 3.7 Aggregate level analyses 3.8 Meta analysis 3.9 Design issues Chapter 4. Multilevel Models for discrete response data 4.1 Generalised linear models 4.2 Proportions as responses 4.3 Examples 4.4 Models for multiple response categories 4.5 Models for counts 4.6 Mixed discrete - continuous response models 4.7 A latent normal model for binary responses 4.8 Partitioning variation in discrete response models Appendix 4.1. Generalised linear model estimation Appendix 4.2 Maximum likelihood estimation for generalised linear models Appendix 4.3 MCMC estimation for generalised linear models Appendix 4.4. Bootstrap estimation for generalised linear models Chapter 5. Models for repeated measures data 5.1 Repeated measures data 5.2 A 2-level repeated measures model 5.3 A polynomial model example for adolescent growth and the prediction of adult height 5.4 Modelling an autocorrelation structure at level 1. 5.5 A growth model with autocorrelated residuals 5.6 Multivariate repeated measures models 5.7 Scaling across time 5.8 Cross-over designs 5.9 Missing data 5.10 Longitudinal discrete response data Chapter 6. Multivariate multilevel data 6.1 Introduction 6.2 The basic 2-level multivariate model 6.3 Rotation Designs 6.4 A rotation design example using Science test scores 6.5 Informative response selection: subject choice in examinations 6.6 Multivariate structures at higher levels and future predictions 6.7 Multivariate responses at several levels 6.8 Principal Components analysis Appendix 6.1 MCMC algorithm for a multivariate normal response model with constraints Chapter 7. Latent normal models for multivariate data 7.1 The normal multilevel multivariate model 7.2 Sampling binary responses 7.3 Sampling ordered categorical responses 7.4 Sampling unordered categorical responses 7.5 Sampling count data 7.6 Sampling continuous non-normal data 7.7 Sampling the level 1 and level 2 covariance matrices 7.8 Model fit 7.9 Partially ordered data 7.10 Hybrid normal/ordered variables 7.11 Discussion Chapter 8. Multilevel factor analysis, structural equation and mixture models 8.1 A 2-stage 2-level factor model 8.2 A general multilevel factor model 8.3 MCMC estimation for the factor model 8.4 Structural equation models 8.5 Discrete response multilevel structural equation models 8.6 More complex hierarchical latent variable models 8.7 Multilevel mixture models Chapter 9. Nonlinear multilevel models 9.1 Introduction 9.2 Nonlinear functions of linear components 9.3 Estimating population means 9.4 Nonlinear functions for variances and covariances 9.5 Examples of nonlinear growth and nonlinear level 1 variance Appendix 9.1 Nonlinear model estimation Chapter 10. Multilevel modelling in sample surveys 10.1 Sample survey structures 10.2 Population structures 10.3 Small area estimation Chapter 11 Multilevel event history and survival models 11.1 Introduction 11.2 Censoring 11.3 Hazard and survival funtions 11.4 Parametric proportional hazard models 11.5 The semiparametric Cox model 11.6 Tied observations 11.7 Repeated events proportional hazard models 11.8 Example using birth interval data 11.9 Log duration models 11.10 Examples with birth interval data and children’s activity episodes 11.11 The grouped discrete time hazards model 11.12 Discrete time latent normal event history models Chapter 12. Cross classified data structures 12.1 Random cross classifications 12.2 A basic cross classified model 12.3 Examination results for a cross classification of schools 12.4 Interactions in cross classifications 12.5 Cross classifications with one unit per cell 12.6 Multivariate cross classified models 12.7 A general notation for cross classifications 12.8 MCMC estimation in cross classified models Appendix 12.1 IGLS Estimation for cross classified data. Chapter 13 Multiple membership models 13.1 Multiple membership structures 13.2 Notation and classifications for multiple membership structures 13.3 An example of salmonella infection 13.4 A repeated measures multiple membership model 13.5 Individuals as higher level units 13.5.1 Example of research grant awards 13.6 Spatial models 13.7 Missing identification models Appendix 13.1 MCMC estimation for multiple membership models. Chapter 14 Measurement errors in multilevel models 14.1 A basic measurement error model 14.2 Moment based estimators 14.3 A 2-level example with measurement error at both levels. 14.4 Multivariate responses 14.5 Nonlinear models 14.6 Measurement errors for discrete explanatory variables 14.7 MCMC estimation for measurement error models Appendix 14.1 Measurement error estimation 14.2 MCMC estimation for measurement error models Chapter 15. Smoothing models for multilevel data. 15.1 Introduction 15.2. Smoothing estimators 15.3 Smoothing splines 15.4 Semi parametric smoothing models 15.5 Multilevel smoothing models 15.6 General multilevel semi-parametric smoothing models 15.7 Generalised linear models 15.8 An example Fixed Random 15.9 Conclusions Chapter 16. Missing data, partially observed data and multiple imputation 16.1 Creating a completed data set 16.2 Joint modelling for missing data 16.3 A two level model with responses of different types at both levels. 16.4 Multiple imputation 16.5 A simulation example of multiple imputation for missing data 16.6 Longitudinal data with attrition 16.7 Partially known data values 16.8 Conclusions Chapter 17 Multilevel models with correlated random effects 17.1 Non-independence of level 2 residuals 17.2 MCMC estimation for non-independent level 2 residuals 17.3 Adaptive proposal distributions in MCMC estimation 17.4 MCMC estimation for non-independent level 1 residuals 17.5 Modelling the level 1 variance as a function of explanatory variables with random effects 17.6 Discrete responses with correlated random effects 17.7 Calculating the DIC statistic 17.8 A growth data set 17.9 Conclusions Chapter 18. Software for multilevel modelling References Author index Subject index

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Book SynopsisThis book takes the novel approach to cover both the sequence and structure analysis of proteins in one volume and from an algorithmic perspective. Key features of the book include:* Provides a comprehensive introduction to the analysis of protein sequence and structure analysis.Table of ContentsPreface. Acknowledgements. Part I: SEQUENCE ANALYSIS. 1. Pairwise Global Alignment of Sequences. 1.1 Alignment and Evolution. 1.2 What is an Alignment? 1.3 A Scoring Scheme for the Model. 1.4 Finding Highest-Scoring Alignments with Dynamic Programming. 1.4.1 Determine Hi,j. 1.4.2 Use of matrices. 1.4.3 Finding the alignments that give the highest score. 1.4.4 Gaps. 1.5 Scoring Matrices. 1.6 Scoring Gaps: Gap Penalties. 1.7 Dynamic Programming for General Gap Penalty. 1.8 Dynamic Programming for Affine Gap Penalty. 1.9 Alignment Score and Sequence Distance. 1.10 Exercises. 1.11 Bibliographic notes. 2 Pairwise Local Alignment and Database Search. 2.1 The Basic Operation: Comparing Two Sequences. 2.2 Dot Matrices. 2.2.1 Filtering. 2.2.2 Repeating segments. 2.3 Dynamic Programming. 2.3.1 Initialization. 2.3.2 Finding the best local alignments. 2.3.3 Algorithms. 2.3.4 Scoring matrices and gap penalties. 2.4 Database Search: BLAST. 2.4.1 The procedure. 2.4.2 Preprocess the query: make the word list. 2.4.3 Scanning the database sequences. 2.4.4 Extending to HSP. 2.4.5 Introducing gaps. 2.4.6 Algorithm. 2.5 Exercises. 2.6 Bibliographic notes. 3. Statistical Analysis. 3.1 Hypothesis Testing for Sequence Homology. 3.1.1 Random generation of sequences. 3.1.2 Use of Z values for estimating the statistical significance. 3.2 Statistical Distributions. 3.2.1 Poisson probability distribution. 3.2.2 Extreme value distributions. 3.3 Theoretical Analysis of Statistical Significance. 3.3.1 The P value has an extreme value distribution. 3.3.2 Theoretical analysis for database search. 3.4 Probability Distributions for Gapped Alignments. 3.5 Assessing and Comparing Programs for Database Search. 3.5.1 Sensitivity and specificity. 3.5.2 Discrimination power. 3.5.3 Using more sequences as queries. 3.6 Exercises. 3.7 Bibliographic notes. 4 .Multiple Global Alignment and Phylogenetic Trees. 4.1 Dynamic Programming. 4.1.1 SP score of multiple alignments. 4.1.2 A pruning algorithm for the DP solution. 4.2 Multiple Alignments and Phylogenetic Trees. 4.3 Phylogeny. 4.3.1 The number of different tree topologies. 4.3.2 Molecular clock theory. 4.3.3 Additive and ultrametric trees. 4.3.4 Different approaches for reconstructing phylogenetic trees. 4.3.5 Distance-based construction. 4.3.6 Rooting of trees. 4.3.7 Statistical test: bootstrapping. 4.4 Progressive Alignment. 4.4.1 Aligning two subset alignments. 4.4.2 Clustering. 4.4.3 Sequence weights. 4.4.4 CLUSTAL. 4.5 Other Approaches. 4.6 Exercises. 4.7 Bibliographic notes. 5. Scoring Matrices. 5.1 Scoring Matrices Based on Physio-Chemical Properties. 5.2 PAM Scoring Matrices. 5.2.1 The evolutionary model. 5.2.2 Calculate substitution matrix. 5.2.3 Matrices for general evolutionary time. 5.2.4 Measuring sequence similarity by use of Mτ. 5.2.5 Odds matrices. 5.2.6 Scoring matrices (log-odds matrices). 5.2.7 Estimating the evolutionary distance. 5.3 BLOSUM Scoring Matrices. 5.3.1 Log-odds matrix. 5.3.2 Developing scoring matrices for different evolutionary distances. 5.4 Comparing BLOSUM and PAM Matrices. 5.5 Optimal Scoring Matrices. 5.5.1 Analysis for one sequence. 5.6 Exercises. 5.7 Bibliographic notes. 6. Profiles. 6.1 Constructing a Profile. 6.1.1 Notation. 6.1.2 Removing rows and columns. 6.1.3 Position weights. 6.1.4 Sequence weights. 6.1.5 Treating gaps. 6.2 Searching Databases with Profiles. 6.3 Iterated BLAST: PSI-BLAST. 6.3.1 Making the multiple alignment. 6.3.2 Constructing the profile. 6.4 HMM Profile. 6.4.1 Definitions for an HMM. 6.4.2 Constructing a profile HMM for a protein family. 6.4.3 Comparing a sequence with an HMM. 6.4.4 Protein family databases. 6.5 Exercises. 6.6 Bibliographic notes. 7. Sequence Patterns. 7.1 The PROSITE Language. 7.2 Exact/Approximate Matching. 7.3 Defining Pattern Classes by Imposing Constraints. 7.4 Pattern Scoring: Information Theory. 7.4.1 Information theory. 7.4.2 Scoring patterns. 7.5 Generalization and Specialization. 7.6 Pattern Discovery: Introduction. 7.7 Comparison-Based Methods. 7.7.1 Pivot-based methods. 7.7.2 Tree progressive methods. 7.8 Pattern-Driven Methods: Pratt. 7.8.1 The main procedure. 7.8.2 Preprocessing. 7.8.3 The pattern space. 7.8.4 Searching. 7.8.5 Ambiguous components. 7.8.6 Specialization. 7.8.7 Pattern scoring. 7.9 Exercises. 7.10 Bibliographic notes. Part II: STRUCTURE ANALYSIS 8. Structures and Structure Descriptions. 8.1 Units of Structure Descriptions. 8.2 Coordinates. 8.3 Distance Matrices. 8.4 Torsion Angles. 8.5 Coarse Level Description. 8.5.1 Line segments (sticks). 8.5.2 Ellipsoid. 8.5.3 Helices. 8.5.4 Strands and sheets. 8.5.5 Topology of Protein Structure (TOPS). 8.6 Identifying the SSEs. 8.6.1 Use of distance matrices. 8.6.2 Define Secondary Structure of Proteins (DSSP). 8.7 Structure Comparison. 8.7.1 Structure descriptions for comparison. 8.7.2 Structure representation. 8.8 Framework for Pairwise Structure Comparison. 8.9 Exercises. 8.10 Bibliographic notes. 9. Superposition and Dynamic Programming. 9.1 Superposition. 9.1.1 Coordinate RMSD. 9.1.2 Distance RMSD. 9.1.3 Using RMSD as scoring of structure similarities. 9.2 Alternating Superposition and Alignment. 9.3 Double Dynamic Programming. 9.3.1 Low-level scoring matrices. 9.3.2 High-level scoring matrix. 9.3.3 Iterated double dynamic programming. 9.4 Similarity of the Methods. 9.5 Exercises. 9.6 Bibliographic notes. 10. Geometric Techniques. 10.1 Geometric Hashing. 10.1.1 Two-dimensional geometric hashing. 10.1.2 Geometric hashing for structure comparison. 10.1.3 Geometric hashing for SSE representation. 10.1.4 Clustering. 10.2 Distance Matrices. 10.2.1 Measuring the similarity of distance (sub)matrices. 10.3 Exercises. 10.4 Bibliographic notes. 11. Clustering: Combining Local Similarities. 11.1 Compatibility and Consistency. 11.2 Searching for Seed Matches. 11.3 Consistency. 11.3.1 Test for consistency. 11.3.2 Overlapping clusters. 11.4 Clustering Algorithms. 11.4.1 Linear clustering. 11.4.2 Hierarchical clustering. 11.5 Clustering by Use of Transformations. 11.5.1 Comparing transformations. 11.5.2 Calculating the new transformation. 11.5.3 Algorithm. 11.6 Clustering by Use of Relations. 11.6.1 How many relations to compare? 11.6.2 Geometric relation. 11.6.3 Distance relation. 11.6.4 Use of graph theory. 11.7 Refinement. 11.8 Exercises. 11.9 Bibliographic notes. 12. Significance and Assessment of Structure Comparisons. 12.1 Constructing Random Structure Models. 12.1.1 Use of distance geometry. 12.2 Use of Structure Databases. 12.2.1 Constructing nonredundant subsets. 12.2.2 Demarcation line for similarity. 12.3 Reversing the Protein Chain. 12.4 Randomized Alignment Models. 12.5 Assessing Comparison and Scoring Methods. 12.6 Is RMSD Suitable for Scoring? 12.7 Scoring and Biological Significance. 12.8 Exercises. 12.9 Bibliographic notes. 13. Multiple Structure Comparison. 13.1 Multiple Superposition. 13.2 Progressive Structure Alignment. 13.2.1 Scoring. 13.2.2 Construction of consensus. 13.3 Finding a Common Core from a Multiple Alignment. 13.4 Discovering Common Cores. 13.4.1 Finding the multiple seed matches. 13.4.2 Pairwise clustering. 13.4.3 Determining common cores. 13.4.4 Scoring clusters. 13.5 Local Structure Patterns. 13.5.1 Local packing patterns. 13.5.2 Discovering packing patterns. 13.5.3 The approach. 13.5.4 Scoring the packing motifs. 13.6 Exercises. 13.7 Bibliographic notes. 14. Protein Structure Classification. 14.1 Protein Domains. 14.2 An Ising Model for Domain Identification. 14.3 Domain Classes. 14.3.1 Mainly-? domains. 14.3.2 Mainly-? domains. 14.3.3 ?–? domains. 14.4 Folds. 14.5 Automatic Approaches to Classification. 14.6 Databases for Structure Classification. 14.7 FSSP-Dali Domain Dictionary. 14.8 CATH. 14.8.1 Domains. 14.8.2 Class. 14.8.3 Architecture. 14.8.4 Topology (fold family). 14.8.5 Homologous superfamily. 14.8.6 Sequence families. 14.8.7 The CATH classification procedure. 14.9 Classification Based on Sticks. 14.10 Exercises. 14.11 Bibliographic notes. Part III: SEQUENCE-STRUCTUREANALYSIS. 15. Structure Prediction: Threading. 15.1 Protein Secondary Structure Prediction. 15.1.1 Artificial neural networks. 15.1.2 The PHD program. 15.1.3 Accuracy in secondary structure prediction. 15.2 Threading. 15.3 Methods Based on Sequence Alignment. 15.3.1 The 3D–1D matching method. 15.3.2 The FUGUE method. 15.4 Methods Using 3D Interactions. 15.4.1 Potentials of mean force. 15.4.2 Towards modelling methods. 15.5 Alignment Methods. 15.5.1 Frozen approximation. 15.5.2 Double Dynamic Programming. 15.6 Multiple Sequence/Structure Threading. 15.6.1 Simple multiple sequence threading. 15.7 Combined Sequence/Threading Methods. 15.8 Assessment of Threading Methods. 15.8.1 Fold recognition. 15.8.2 Alignment accuracy. 15.8.3 CASP and CAFASP. 15.9 Bibliographic notes. Appendix A: Basics in Mathematics, Probability and Algorithms. A.1 Mathematical Formulae and Notation. A.2 Boolean Algebra. A.3 Set Theory. A.4 Probability. A.4.1 Permutation and combination. A.4.2 Probability distributions. A.4.3 Expected value. A.5 Tables, Vectors and Matrices. A.6 Algorithmic Language. A.6.1 Alternatives. A.6.2 Loops. A.7 Complexity. Appendix B: Introduction to Molecular Biology. B.1 The Cell and the Molecules of Life: DNA–RNA Proteins. B.2 Chromosomes and Genes. B.3 The Central Dogma of Molecular Biology. B.4 The Genetic Code. B.5 Protein Function. B.5.1 The gene ontology. B.6 Protein Structure. B.7 Evolution. B.8 Insulin Example. B.9 Bibliographic notes. References. Index.

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Book SynopsisFeatures coverage of the epidemiological indices, and includes developments in the field. This title serves as a useful reference source for biostatisticians and epidemiologists working in disease prevention, as the chapters are self-contained and feature several real examples.Trade Review"…a concise, organized, and well-written text that provides the derivations of statistical formulas underlying much epidemiological research and practice." (Journal of the American Statistical Association, December 2005) "...presents a considerable amount of recent research, much of which is the author's own..." (Royal Statistical Society, Vol.168, No.1, January 2005) "...systematically organised...an excellent reference..." (Short Book Review, Vol.24, No.3 December 2004) "...this book is strongly recommended..." (Statistical Methods in Medical Research, Vol 14 2005)Table of ContentsAbout the author. Preface. 1 Population Proportion or Prevalence. 1.1 Binomial sampling. 1.2 Cluster sampling. 1.3 Inverse sampling. Exercises. References. 2 Risk Difference. 2.1 Independent binomial sampling. 2.2 A series of independent binomial sampling procedures. 2.2.1 Summary interval estimators. 2.2.2 Test for the homogeneity of risk difference. 2.3 Independent cluster sampling. 2.4 Paired-sample data. 2.5 Independent negative binomial sampling (inverse sampling). 2.6 Independent poisson sampling. 2.7 Stratified poisson sampling. Exercises. References. 3 Relative Difference. 3.1 Independent binomial sampling. 3.2 A series of independent binomial sampling procedures. 3.2.1 Asymptotic interval estimators. 3.2.2 Test for the homogeneity of relative difference. 3.3 Independent cluster sampling. 3.4 Paired-sample data. 3.5 Independent inverse sampling. Exercises. References. 4 Relative Risk. 4.1 Independent binomial sampling. 4.2 A series of independent binomial sampling procedures. 4.2.1 Asymptotic interval estimators. 4.2.2 Test for the homogeneity of risk ratio. 4.3 Independent cluster sampling. 4.4 Paired-sample data. 4.5 Independent inverse sampling. 4.5.1 Uniformly minimum variance unbiased estimator of relative risk. 4.5.2 Interval estimators of relative risk. 4.6 Independent poisson sampling. 4.7 Stratified poisson sampling. Exercises. References. 5 Odds Ratio. 5.1 Independent binomial sampling. 5.1.1 Asymptotic interval estimators. 5.1.2 Exact confidence interval. 5.2 A series of independent binomial sampling procedures. 5.2.1 Asymptotic interval estimators. 5.2.2 Exact confidence interval. 5.2.3 Test for homogeneity of the odds ratio. 5.3 Independent cluster sampling. 5.4 One-to-one matched sampling. 5.5 Logistic modeling. 5.5.1 Estimation under multinomial or independent binomial sampling. 5.5.2 Estimation in the case of paired-sample data. 5.6 Independent inverse sampling. 5.7 Negative multinomial sampling for paired-sample data. Exercises. References. 6 Generalized Odds Ratio. 6.1 Independent multinomial sampling. 6.2 Data with repeated measurements (or under cluster sampling). 6.3 Paired-sample data. 6.4 Mixed negative multinomial and multinomial sampling. Exercises. References. 7 Attributable Risk. 7.1 Study designs with no confounders. 7.1.1 Cross-sectional sampling. 7.1.2 Case–control studies. 7.2 Study designs with confounders. 7.2.1 Cross-sectional sampling. 7.2.2 Case–control studies. 7.3 Case–control studies with matched pairs. 7.4 Multiple levels of exposure in case–control studies. 7.5 Logistic modeling in case–control studies. 7.5.1 Logistic model containing only the exposure variables of interest. 7.5.2 Logistic regression model containing both exposure and confounding variables. 7.6 Case–control studies under inverse sampling. Exercises. References. 8 Number Needed to Treat. 8.1 Independent binomial sampling. 8.2 A series of independent binomial sampling procedures. 8.3 Independent cluster sampling. 8.4 Paired-sample data. Exercises. References. Appendix Maximum Likelihood Estimator and Large-Sample Theory. A.1: The maximum likelihood estimator, Wald’s test, the score test, and the asymptotic likelihood ratio test. A.2: The delta method and its applications. References. Answers to Selected Exercises. Index.

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Book SynopsisPresents the fundamentals in probability and statistics along with relevant applications. This book explains the concept of probabilistic modelling and the process of model selection, verification and analysis. It also demonstrates practical problem solving with examples and exercises.Trade Review“For most practising engineers, this book would make a superb reference text, simply because there are so many worked examples, all extremely relevant to engineers.” (Significance, 1 March 2005) Table of ContentsPreface. 1. Introduction. Part A: Probability and Random Variables. 2. Basic Probability Concepts. 3. Random Variables and Probability Distributions. 4. Expectations And Moments. 5. Functions of Random Variables. 6. Some Important Discrete Distributions. 7. Some Important Continuous Distributions. Part B: Statistical Inference, Parameter Estimation, and Model Verification. 8. Observed Data and Graphical Representation. 9. Parameter Estimation. 10. Model Verification. 11. Linear Models and Linear Regression. Appendix A: Tables. Appendix B: Computer Software. Appendix C: Answers to Selected Problems. Subject Index.

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Book SynopsisPresents the fundamentals of the subject along with concepts of probabilistic modelling, and the process of model selection, verification and analysis. This book includes more than 100 examples and 200 exercises, along with a solutions manual for instructors. It presents the fundamentals in probability and statistics along with their applications.Trade Review“For most practising engineers, this book would make a superb reference text, simply because there are so many worked examples, all extremely relevant to engineers.” (Significance, 1 March 2005) "...the many engineering related examples and exercise problems are a strong feature..." (Technometrics, May 2005) "...designed for students, and as reference for lecturers, the book provides a comprehensive understanding of probability and statistics..." (New Civil Engineer, 18 March, 2004) "...written in an accessible and clear way...gives important techniques of the basic standard methods." (Zentralblatt Math, Vol.1049 2004) "...a good introduction to the ideas of probability and statistics...I would recommend it to anyone as a reference for basic theory..." (Journal of Applied Statistics, Vol 32 (6) August 2005)Table of ContentsPreface. 1. Introduction. Part A: Probability and Random Variables. 2. Basic Probability Concepts. 3. Random Variables and Probability Distributions. 4. Expectations And Moments. 5. Functions of Random Variables. 6. Some Important Discrete Distributions. 7. Some Important Continuous Distributions. Part B: Statistical Inference, Parameter Estimation, and Model Verification. 8. Observed Data and Graphical Representation. 9. Parameter Estimation. 10. Model Verification. 11. Linear Models and Linear Regression. Appendix A: Tables. Appendix B: Computer Software. Appendix C: Answers to Selected Problems. Subject Index.

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Book SynopsisPraise for the First Edition . . . an excellent textbook . . . well organized and neatly written. Mathematical Reviews . . . amazingly interesting . . . Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers'' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statiTable of ContentsPreface xi Preface to the First Edition xiii 1 Basic Probability Theory 1 1.1 Introduction 1 1.2 Sample Spaces and Events 3 1.3 The Axioms of Probability 7 1.4 Finite Sample Spaces and Combinatorics 15 1.4.1 Combinatorics 17 1.5 Conditional Probability and Independence 27 1.6 The Law of Total Probability and Bayes’ Formula 41 Problems 63 2 Random Variables 76 2.1 Introduction 76 2.2 Discrete Random Variables 77 2.3 Continuous Random Variables 82 2.4 Expected Value and Variance 95 2.5 Special Discrete Distributions 111 2.6 The Exponential Distribution 123 2.7 The Normal Distribution 127 2.8 Other Distributions 131 2.9 Location Parameters 137 2.10 The Failure Rate Function 139 Problems 144 3 Joint Distributions 156 3.1 Introduction 156 3.2 The Joint Distribution Function 156 3.3 Discrete Random Vectors 158 3.4 Jointly Continuous Random Vectors 160 3.5 Conditional Distributions and Independence 164 3.5.1 Independent Random Variables 168 3.6 Functions of Random Vectors 172 3.7 Conditional Expectation 185 3.8 Covariance and Correlation 196 3.9 The Bivariate Normal Distribution 209 3.10 Multidimensional Random Vectors 216 3.11 Generating Functions 231 3.12 The Poisson Process 240 Problems 247 4 Limit Theorems 263 4.1 Introduction 263 4.2 The Law of Large Numbers 264 4.3 The Central Limit Theorem 268 4.4 Convergence in Distribution 275 Problems 278 5 Simulation 281 5.1 Introduction 281 5.2 Random Number Generation 282 5.3 Simulation of Discrete Distributions 283 5.4 Simulation of Continuous Distributions 285 5.5 Miscellaneous 290 Problems 292 6 Statistical Inference 294 6.1 Introduction 294 6.2 Point Estimators 294 6.3 Confidence Intervals 304 6.4 Estimation Methods 312 6.5 Hypothesis Testing 327 6.6 Further Topics in Hypothesis Testing 334 6.7 Goodness of Fit 339 6.8 Bayesian Statistics 351 6.9 Nonparametric Methods 363 Problems 378 7 Linear Models 391 7.1 Introduction 391 7.2 Sampling Distributions 392 7.3 Single Sample Inference 395 7.4 Comparing Two Samples 402 7.5 Analysis of Variance 409 7.6 Linear Regression 415 7.7 The General Linear Model 431 Problems 436 8 Stochastic Processes 444 8.1 Introduction 444 8.2 Discrete -Time Markov Chains 445 8.3 Random Walks and Branching Processes 464 8.4 Continuous -Time Markov Chains 475 8.5 Martingales 494 8.6 Renewal Processes 502 8.7 Brownian Motion 509 Problems 517 Appendix A Tables 527 Appendix B Answers to Selected Problems 535 Further Reading 551 Index 553

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Book SynopsisA complete set of statistical tools for beginning financial analysts from a leading authority Written by one of the leading experts on the topic, An Introduction to Analysis of Financial Data with R explores basic concepts of visualization of financial data. Through a fundamental balance between theory and applications, the book supplies readers with an accessible approach to financial econometric models and their applications to real-world empirical research. The author supplies a hands-on introduction to the analysis of financial data using the freely available R software package and case studies to illustrate actual implementations of the discussed methods. The book begins with the basics of financial data, discussing their summary statistics and related visualization methods. Subsequent chapters explore basic time series analysis and simple econometric models for business, finance, and economics as well as related topics including: LinearTrade Review“I found this book highly informative and interesting to read. The proper mix of theory and hands-on programming examples makes it recommended reading for both R programmers interested in finance and financial analysts with a basic programming background. Well written and following a clear and defined logical layout, the author has written a current reference text on using a powerful open-source programming language for typical financial analysis.” (Computing Reviews, 25 March 2014) “All in all, this book is a good and useful introduction to financial time series with many real-world examples. It is suitable for use both as a textbook and for self-study, with exercises provided at the end of each chapter.” (International Statistical Review, 14 June 2013) Table of ContentsPreface xiii 1 FINANCIAL DATA AND THEIR PROPERTIES 1 1.1 Asset Returns 2 1.2 Bond Yields and Prices 7 1.3 Implied Volatility 10 1.4 R Packages and Demonstrations 12 1.4.1 Installation of R Packages 12 1.4.2 The Quantmod Package 12 1.4.3 Some Basic R Commands 16 1.5 Examples of Financial Data 17 1.6 Distributional Properties of Returns 20 1.6.1 Review of Statistical Distributions and Their Moments 20 1.7 Visualization of Financial Data 27 1.8 Some Statistical Distributions 32 1.8.1 Normal Distribution 32 1.8.2 Lognormal Distribution 32 1.8.3 Stable Distribution 33 1.8.4 Scale Mixture of Normal Distributions 33 1.8.5 Multivariate Returns 34 Exercises 36 References 37 2 LINEAR MODELS FOR FINANCIAL TIME SERIES 39 2.1 Stationarity 40 2.2 Correlation and Autocorrelation Function 43 2.3 White Noise and Linear Time Series 50 2.4 Simple Autoregressive Models 51 2.4.1 Properties of AR Models 52 2.4.2 Identifying AR Models in Practice 60 2.4.3 Goodness of Fit 67 2.4.4 Forecasting 67 2.5 Simple Moving Average Models 69 2.5.1 Properties of MA Models 72 2.5.2 Identifying MA Order 73 2.5.3 Estimation 74 2.5.4 Forecasting Using MA Models 75 2.6 Simple ARMA Models 78 2.6.1 Properties of ARMA(1,1) Models 79 2.6.2 General ARMA Models 80 2.6.3 Identifying ARMA Models 81 2.6.4 Forecasting Using an ARMA Model 84 2.6.5 Three Model Representations for an ARMA Model 84 2.7 Unit-Root Nonstationarity 86 2.7.1 Random Walk 86 2.7.2 Random Walk with Drift 88 2.7.3 Trend-Stationary Time Series 90 2.7.4 General Unit-Root Nonstationary Models 91 2.7.5 Unit-Root Test 91 2.8 Exponential Smoothing 96 2.9 Seasonal Models 98 2.9.1 Seasonal Differencing 99 2.9.2 Multiplicative Seasonal Models 101 2.9.3 Seasonal Dummy Variable 107 2.10 Regression Models with Time Series Errors 110 2.11 Long-Memory Models 117 2.12 Model Comparison and Averaging 120 2.12.1 In-sample Comparison 120 2.12.2 Out-of-sample Comparison 121 2.12.3 Model Averaging 125 Exercises 125 References 127 3 CASE STUDIES OF LINEAR TIME SERIES 128 3.1 Weekly Regular Gasoline Price 129 3.1.1 Pure Time Series Model 130 3.1.2 Use of Crude Oil Prices 133 3.1.3 Use of Lagged Crude Oil Prices 134 3.1.4 Out-of-Sample Predictions 135 3.2 Global Temperature Anomalies 140 3.2.1 Unit-Root Stationarity 141 3.2.2 Trend-Nonstationarity 145 3.2.3 Model Comparison 148 3.2.4 Long-Term Prediction 150 3.2.5 Discussion 153 3.3 US Monthly Unemployment Rates 157 3.3.1 Univariate Time Series Models 157 3.3.2 An Alternative Model 161 3.3.3 Model Comparison 165 3.3.4 Use of Initial Jobless Claims 165 3.3.5 Comparison 173 Exercises 174 References 175 4 ASSET VOLATILITY AND VOLATILITY MODELS 176 4.1 Characteristics of Volatility 177 4.2 Structure of a Model 178 4.3 Model Building 181 4.4 Testing for ARCH Effect 182 4.5 The ARCH Model 185 4.5.1 Properties of ARCH Models 186 4.5.2 Advantages and Weaknesses of ARCH Models 187 4.5.3 Building an ARCH Model 188 4.5.4 Some Examples 193 4.6 The GARCH Model 199 4.6.1 An Illustrative Example 201 4.6.2 Forecasting Evaluation 210 4.6.3 A Two-Pass Estimation Method 210 4.7 The Integrated GARCH Model 211 4.8 The GARCH-M Model 213 4.9 The Exponential Garch Model 215 4.9.1 An Illustrative Example 217 4.9.2 An Alternative Model Form 218 4.9.3 Second Example 218 4.9.4 Forecasting Using an EGARCH Model 220 4.10 The Threshold Garch Model 222 4.11 Asymmetric Power ARCH Models 224 4.12 Nonsymmetric GARCH Model 226 4.13 The Stochastic Volatility Model 228 4.14 Long-Memory Stochastic Volatility Models 230 4.15 Alternative Approaches 232 4.15.1 Use of High Frequency Data 232 4.15.2 Use of Daily Open, High, Low, and Close Prices 235 Exercises 239 References 241 5 APPLICATIONS OF VOLATILITY MODELS 243 5.1 Garch Volatility Term Structure 244 5.1.1 Term Structure 246 5.2 Option Pricing and Hedging 248 5.3 Time-Varying Correlations and Betas 251 5.3.1 Time-Varying Betas 256 5.4 Minimum Variance Portfolios 259 5.5 Prediction 263 Exercises 271 References 272 6 HIGH FREQUENCY FINANCIAL DATA 274 6.1 Nonsynchronous Trading 275 6.2 Bid–Ask Spread of Trading Prices 279 6.3 Empirical Characteristics of Trading Data 282 6.4 Models for Price Changes 285 6.4.1 Ordered Probit Model 288 6.4.2 A Decomposition Model 293 6.5 Duration Models 298 6.5.1 Diurnal Component 299 6.5.2 The ACD Model 301 6.5.3 Estimation 303 6.6 Realized Volatility 308 6.6.1 Handling Microstructure Noises 313 6.6.2 Discussion 317 Appendix A: Some Probability Distributions 320 Appendix B: Hazard Function 323 Exercises 324 References 325 7 VALUE AT RISK 327 7.1 Risk Measure and Coherence 328 7.1.1 Value at Risk (VaR) 329 7.1.2 Expected Shortfall 334 7.2 Remarks on Calculating Risk Measures 336 7.3 Riskmetrics 337 7.3.1 Discussion 342 7.3.2 Multiple Positions 343 7.4 An Econometric Approach 345 7.4.1 Multiple Periods 348 7.5 Quantile Estimation 352 7.5.1 Quantile and Order Statistics 353 7.5.2 Quantile Regression 354 7.6 Extreme Value Theory 358 7.6.1 Review of Extreme Value Theory 358 7.6.2 Empirical Estimation 361 7.6.3 Application to Stock Returns 363 7.7 An Extreme Value Approach to Var 368 7.7.1 Discussion 370 7.7.2 Multiperiod VaR 371 7.7.3 Return Level 371 7.8 Peaks Over Thresholds 372 7.8.1 Statistical Theory 373 7.8.2 Mean Excess Function 374 7.8.3 Estimation 376 7.8.4 An Alternative Parameterization 378 7.9 The Stationary Loss Processes 381 Exercises 383 References 384 Index 387

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Book Synopsis* Montgomery, Runger, and Hubele provide modern coverage of engineering statistics, focusing on how statistical tools are integrated into the engineering problem-solving process.

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Book SynopsisAn insightful, hands-on focus on the statistical methods used by compensation and human resources professionals in their everyday work Across various industries, compensation professionals work to organize and analyze aspects of employment that deal with elements of pay, such as deciding base salary, bonus, and commission provided by an employer to its employees for work performed. Acknowledging the numerous quantitative analyses of data that are a part of this everyday work, Statistics for Compensation provides a comprehensive guide to the key statistical tools and techniques needed to perform those analyses and to help organizations make fully informed compensation decisions. This self-contained book is the first of its kind to explore the use of various quantitative methodsfrom basic notions about percents to multiple linear regressionthat are used in the management, design, and implementation of powerful compensation strategies. Drawing upon his exteTrade Review“As an experienced compensation manager for a publicly traded Fortune 500 company, I have found this book to be an all-inclusive, highly useful and infor­mative desk reference. It certainly has been extremely valuable in helping me to contribute to successful strategic decisions at my company.” (Workspan, 1 January 2013) "The book can serve as a text for students specializing in compensation or human resources, or as a reference for practitioners. He provides worked examples throughout." (Booknews, 1 June 2011) Table of ContentsPreface xiii Chapter 1 Introduction 1 1.1 Why do Statistical Analysis? 2 Example Analysis 3 1.2 Statistics 5 1.3 Numbers Raise Issues 6 1.4 Behind Every Data Point, There Is a Story 8 1.5 Aggressive Inquisitiveness 9 1.6 Model Building Framework 9 Example Model 10 1.7 Data Sets 10 1.8 Prerequisites 11 Chapter 2 Basic Notions 13 2.1 Percent 14 Graphical Displays of Percents 16 2.2 Percent Difference 21 2.3 Compound Interest 23 Future Value 24 Present Value 26 Translating 27 Practice Problems 28 Chapter 3 Frequency Distributions and Histograms 31 3.1 Definitions and Construction 41 Rules for Categories 43 3.2 Comparing Distributions 48 Absolute Comparison and Relative Comparison 48 Comparing More Than Two Distributions 50 3.3 Information Loss and Comprehension Gain 51 3.4 Category Selection 51 3.5 Distribution Shapes 54 Uniform Distribution 55 Bell-Shaped Distribution 55 Normal Distribution 56 Skewed Distribution 59 Bimodal Distribution 60 Practice Problems 62 Chapter 4 Measures of Location 67 4.1 Mode 67 4.2 Median 68 4.3 Mean 70 4.4 Trimmed Mean 73 4.5 Overall Example and Comparison 73 Comparison 75 4.6 Weighted and Unweighted Average 76 Which Measure to Use? 78 Application of Weighted Averages to Salary Increase Guidelines 80 4.7 Simpson’s Paradox 82 4.8 Percentile 85 Reverse Percentile 88 4.9 Percentile Bars 90 Practice Problems 92 Chapter 5 Measures of Variability 95 5.1 Importance of Knowing Variability 95 5.2 Population and Sample 96 Examples of Populations 96 Examples of Samples and Populations 96 5.3 Types of Samples 97 5.4 Standard Deviation 98 Interpretations and Applications of Standard Deviation 100 5.5 Coefficient of Variation 107 Interpretations and Applications of Coefficient of Variation 108 5.6 Range 109 Interpretations and Applications of Range 109 5.7 P90/P10 110 Interpretations and Applications of P90/P10 111 5.8 Comparison and Summary 112 Practice Problems 115 Chapter 6 Model Building 119 6.1 Prelude to Models 119 6.2 Introduction 120 6.3 Scientific Method 122 6.4 Models 123 6.5 Model Building Process 126 Plotting Points 128 Functional Forms 132 Method of Least Squares 136 Practice Problems 138 Chapter 7 Linear Model 141 7.1 Examples 141 7.2 Straight Line Basics 143 Interpretations of Intercept and Slope 144 Using the Equation 145 7.3 Fitting the Line to the Data 147 What We Are Predicting 148 Interpretations of Intercept and Slope 149 7.4 Model Evaluation 149 Appearance 150 Coefficient of Determination 150 Correlation 152 Standard Error of Estimate 154 Common Sense 154 7.5 Summary of Interpretations and Evaluation 155 7.6 Cautions 155 7.7 Digging Deeper 158 7.8 Keep the Horse before the Cart 160 Practice Problems 164 Chapter 8 Exponential Model 167 8.1 Examples 167 8.2 Logarithms 168 Antilogs 170 Scales 170 Why Logarithms? 171 8.3 Exponential Model 172 8.4 Model Evaluation 176 Appearance 176 Coefficient of Determination 177 Correlation 177 Standard Error of Estimate 177 Common Sense 178 Summary of Evaluation 178 Practice Problems 178 Chapter 9 Maturity Curve Model 181 9.1 Maturity Curves 181 9.2 Building the Model 184 Cubic Model 184 Cubic Model Evaluation 186 Spline Model 187 Spline Model Evaluation 188 9.3 Comparison of Models 190 Practice Problems 190 Chapter 10 Power Model 193 10.1 Building the Model 193 10.2 Model Evaluation 197 Appearance 197 Coefficient of Determination 198 Correlation 198 Standard Error of Estimate 198 Common Sense 199 Summary of Evaluation 199 Practice Problems 200 Chapter 11 Market Models and Salary Survey Analysis 201 11.1 Introduction 201 11.2 Commonalities of Approaches 203 11.3 Final Market-Based Salary Increase Budget 205 Initial Market-Based Salary Increase Budget and Market Position 205 Final Market-Based Salary Increase Budget 206 Raises Given Throughout the Year 206 Raises Given on a Common Date 208 11.4 Other Factors Influencing the Final Salary Increase Budget Recommendation 210 Assumptions 211 11.5 Salary Structure 211 Practice Problems 213 Chapter 12 Integrated Market Model: Linear 215 12.1 Gather Market Data 215 12.2 Age Data to a Common Date 217 12.3 Create an Integrated Market Model 217 Interpretations 219 12.4 Compare Employee Pay with Market Model 222 Practice Problems 228 Chapter 13 Integrated Market Model: Exponential 233 Practice Problems 246 Chapter 14 Integrated Market Model: Maturity Curve 251 Practice Problems 261 Chapter 15 Job Pricing Market Model: Group of Jobs 265 Practice Problems 272 Chapter 16 Job Pricing Market Model: Power Model 277 Practice Problems 280 Chapter 17 Multiple Linear Regression 283 17.1 What It Is 283 17.2 Similarities and Differenceswith Simple Linear Regression 284 17.3 Building the Model 285 First x-Variable 292 Second x-Variable 295 Standardized Coefficient 298 Third x-Variable 300 Multicollinearity 301 17.4 Model Evaluation 305 Regression Coefficients 305 Standardized Coefficients 306 Coefficient of Determination 306 Standard Error of Estimate 306 Multicollinearity 306 Simplicity 307 Common Sense 307 Acceptability 307 Reality 307 Decision 307 17.5 Mixed Messages in Evaluating A Model 308 r2 Versus Common Sense 308 r2 Versus Simplicity 308 Simplicity Versus Acceptability 308 17.6 Summary of Regressions 308 17.7 Digging Deeper 310 Summary 315 Practice Problems 317 Appendix 319 A.1 Value Exchange Theory 319 Achieving Organization Goals 319 Value Exchange 319 A Fair Value Exchange Is a Good Deal 320 A.2 Factors Determining a Person’s Pay 321 System Factors 322 Individual Factors 323 A.3 Types of Numbers 324 Definitions and Properties 324 Histograms with All Four Types of Measurements 327 A.4 Significant Figures 330 A.5 Scientific Notation 331 A.6 Accuracy and Precision 332 Which Is More Important? 333 A.7 Compound Interest–Additional 333 Other Formulas 333 A.8 Rule of 72 334 Derivation of the Rule of 72 335 A.9 Normal Distribution 336 Central Limit Theorem 337 Distribution of Salary Survey Data 338 A.10 Linear Regression Technical Note 338 A.11 Formulas for Regression Terms 340 A.12 Logarithmic Conversion 340 A.13 Range Spread Relationships 340 Overlap 343 A.14 Statistical Inference in Regression 344 t-Statistic and Its Probability 347 F-Statistic and Its Probability 348 Mixed Messages in Evaluating a Model 349 A.15 Additional Multiple Linear Regression Topics 349 Adjusted r2 349 Coding of Indicator Variables 350 Interaction Terms 351 GLOSSARY 357 REFERENCES 369 ANSWERS TO PRACTICE PROBLEMS 371 INDEX 433

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Book SynopsisStatistics in Psychology covers all statistical methods needed in education and research in psychology. This book looks at research questions when planning data sampling, that is to design the intended study and to calculate the sample sizes in advance.Table of ContentsIntroduction. 1 Concept of the Book. 2 Measuring in Psychology. 2.1 Types of psychological measurements. 2.2 Measurement techniques in psychological assessment. 2.3 Quality criteria in psychometrics. 2.4 Additional psychological measurement techniques. 2.5 Statistical models of measurement with psychological roots. 3 Psychology: An Empirical Science. 3.1 Gain of insight in psychology. 3.2 Steps of empirical research. 4 Definition: Character, Chance, Experiment, and Survey. 4.1 Nominal scale. 4.2 Ordinal scale. 4.3 Interval scale. 4.4 Ratio scale. 4.5 Characters and factors. II Descriptive Statistics. 5 Numerical and graphical Data Analysis. 5.1 Introduction to data analysis. 5.2 Frequencies and empirical distributions. 5.3 Statistics. 5.4 Frequency distribution for several characters. III Inferential Statistics for one Character. 6 Probability and distribution. 6.1 Relative frequencies and probabilities. 6.2 Random variable and theoretical distributions. 6.3 Quantiles of theoretical distribution functions. 6.4 Mean and variance of theoretical distributions. 6.5 Estimation of unknown parameters. 7 Assumptions: Random Sampling and Randomization. 7.1 Simple random sampling in surveys. 7.2 Principles of random sampling and randomization. 8 One Sample from one Population. 8.1 Introduction. 8.2 The Parameter mof acharacter modeled by a normally distributed random variable. 8.3 Planning a study for hypothesis testing with respect to m. 8.4 Sequential tests for the unknown parameter m. 8.5 Estimation, hypothesis testing, planning the study, and sequential testing concerning other parameters. 9 Two Samples from two Populations. 9.1 Hypothesis testing, study planning and sequential testing regarding the unknown parameters m1 and m2. 9.2 Hypothesis testing, study planning and sequential testing for other parameters. 9.3 Equivalence testing. 10 Samples from more than two Populations. 10.1 The various problem situations. 10.2. Selection procedures. 10.3 Multiple comparisons of means. 10.4 Analysis of variance. IV Descriptive and Inferential Statistics for two Characters. 11 Regression and Correlation. 11.1 Introduction. 11.2 Regression model. 11.3 Correlation coefficients and measures of association. 11.4 Hypothesis testing and planning the study concerning correlation coefficients. 11.5 Correlation analysis in two samples. V Inferential Statistics for more than two Characters. 12 One Sample from one Population. 12.1 Association between three or more characters. 12.2 Hypothesis testing concerning a vector of means m. 12.3 Comparisons of means and "homological" methods for matched observations. 13 Samples from more than one Population. 13.1 General linear model. 13.2 Analysis of covariance. 13.3. Multivariate analysis of variance. 13.4 Discriminant analysis. VI Model Generation and Theory-Generating Procedures. 14 Model Generation. 14.1 Theoretical basics of model generation. 14.2 Methods for determining the quality and excellence of a model. 14.2.1 Goodness of fit tests. 14.2.2 Coefficients of the goodness of fit. 14.2.3 Cross-validation. 14.4 Simulation: Non-analytical solutions to statistical problems. 15 Theory-Generating Procedures. 15.1 Descriptive statistics' methods. 15.2 Methods of inferential statistics.

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Book SynopsisModern Analysis of Customer Surveys: with applications using R Customer survey studies deal with customer, consumer and user satisfaction from a product or service. In practice, many of the customer surveys conducted by business and industry are analyzed in a very simple way, without using models or statistical methods. Typical reports include descriptive statistics and basic graphical displays. This book demonstrates how integrating such basic analysis with more advanced tools, provides insights into non-obvious patterns and important relationships between the survey variables. This knowledge can significantly affect the conclusions derived from a survey. Key features: Provides an integrated case studies-based approach to analysing customer survey data. Presents a general introduction to customer surveys, within an organization's business cycle. Contains classical techniques with modern and non standard tools.Table of ContentsForeword xvii Preface xix Contributors xxiii Part I Basic Aspects of Customer Satisfaction Survey Data Analysis 1 Standards and Classical Techniques in Data Analysis of Customer Satisfaction Surveys 3 Silvia Salini and Ron S. Kenett 1.1 Literature on customer satisfaction surveys 4 1.2 Customer satisfaction surveys and the business cycle 4 1.3 Standards used in the analysis of survey data 7 1.4 Measures and models of customer satisfaction 12 1.4.1 The conceptual construct 12 1.4.2 The measurement process 13 1.5 Organization of the book 15 1.6 Summary 17 References 17 2 The ABC Annual Customer Satisfaction Survey 19 Ron S. Kenett and Silvia Salini 2.1 The ABC company 19 2.2 ABC 2010 ACSS: Demographics of respondents 20 2.3 ABC 2010 ACSS: Overall satisfaction 22 2.4 ABC 2010 ACSS: Analysis of topics 24 2.5 ABC 2010 ACSS: Strengths and weaknesses and decision drivers 27 2.6 Summary 28 References 28 Appendix 29 3 Census and Sample Surveys 37 Giovanna Nicolini and Luciana Dalla Valle 3.1 Introduction 37 3.2 Types of surveys 39 3.2.1 Census and sample surveys 39 3.2.2 Sampling design 40 3.2.3 Managing a survey 40 3.2.4 Frequency of surveys 41 3.3 Non-sampling errors 41 3.3.1 Measurement error 42 3.3.2 Coverage error 42 3.3.3 Unit non-response and non-self-selection errors 43 3.3.4 Item non-response and non-self-selection error 44 3.4 Data collection methods 44 3.5 Methods to correct non-sampling errors 46 3.5.1 Methods to correct unit non-response errors 46 3.5.2 Methods to correct item non-response 49 3.6 Summary 51 References 52 4 Measurement Scales 55 Andrea Bonanomi and Gabriele Cantaluppi 4.1 Scale construction 55 4.1.1 Nominal scale 56 4.1.2 Ordinal scale 57 4.1.3 Interval scale 58 4.1.4 Ratio scale 59 4.2 Scale transformations 60 4.2.1 Scale transformations referred to single items 61 4.2.2 Scale transformations to obtain scores on a unique interval scale 66 Acknowledgements 69 References 69 5 Integrated Analysis 71 Silvia Biffignandi 5.1 Introduction 71 5.2 Information sources and related problems 73 5.2.1 Types of data sources 73 5.2.2 Advantages of using secondary source data 73 5.2.3 Problems with secondary source data 74 5.2.4 Internal sources of secondary information 75 5.3 Root cause analysis 78 5.3.1 General concepts 78 5.3.2 Methods and tools in RCA 81 5.3.3 Root cause analysis and customer satisfaction 85 5.4 Summary 87 Acknowledgement 87 References 87 6 Web Surveys 89 Roberto Furlan and Diego Martone 6.1 Introduction 89 6.2 Main types of web surveys 90 6.3 Economic benefits of web survey research 91 6.3.1 Fixed and variable costs 92 6.4 Non-economic benefits of web survey research 94 6.5 Main drawbacks of web survey research 96 6.6 Web surveys for customer and employee satisfaction projects 100 6.7 Summary 102 References 102 7 The Concept and Assessment of Customer Satisfaction 107 Irena Ograjenšek and Iddo Gal 7.1 Introduction 107 7.2 The quality–satisfaction–loyalty chain 108 7.2.1 Rationale 108 7.2.2 Definitions of customer satisfaction 108 7.2.3 From general conceptions to a measurement model of customer satisfaction 110 7.2.4 Going beyond SERVQUAL: Other dimensions of relevance to the B2B context 112 7.2.5 From customer satisfaction to customer loyalty 113 7.3 Customer satisfaction assessment: Some methodological considerations 115 7.3.1 Rationale 115 7.3.2 Think big: An assessment programme 115 7.3.3 Back to basics: Questionnaire design 116 7.3.4 Impact of questionnaire design on interpretation 118 7.3.5 Additional concerns in the B2B setting 119 7.4 The ABC ACSS questionnaire: An evaluation 119 7.4.1 Rationale 119 7.4.2 Conceptual issues 119 7.4.3 Methodological issues 120 7.4.4 Overall ABC ACSS questionnaire asssessment 121 7.5 Summary 121 References 122 Appendix 126 8 Missing Data and Imputation Methods 129 Alessandra Mattei, Fabrizia Mealli and Donald B. Rubin 8.1 Introduction 129 8.2 Missing-data patterns and missing-data mechanisms 131 8.2.1 Missing-data patterns 131 8.2.2 Missing-data mechanisms and ignorability 132 8.3 Simple approaches to the missing-data problem 134 8.3.1 Complete-case analysis 134 8.3.2 Available-case analysis 135 8.3.3 Weighting adjustment for unit nonresponse 135 8.4 Single imputation 136 8.5 Multiple imputation 138 8.5.1 Multiple-imputation inference for a scalar estimand 138 8.5.2 Proper multiple imputation 139 8.5.3 Appropriately drawing imputations with monotone missing-data patterns 140 8.5.4 Appropriately drawing imputations with nonmonotone missing-data patterns 141 8.5.5 Multiple imputation in practice 142 8.5.6 Software for multiple imputation 143 8.6 Model-based approaches to the analysis of missing data 144 8.7 Addressing missing data in the ABC annual customer satisfaction survey: An example 145 8.8 Summary 149 Acknowledgements 150 References 150 9 Outliers and Robustness for Ordinal Data 155 Marco Riani, Francesca Torti and Sergio Zani 9.1 An overview of outlier detection methods 155 9.2 An example of masking 157 9.3 Detection of outliers in ordinal variables 159 9.4 Detection of bivariate ordinal outliers 160 9.5 Detection of multivariate outliers in ordinal regression 161 9.5.1 Theory 161 9.5.2 Results from the application 163 9.6 Summary 168 References 168 Part II Modern Techniques in Customer Satisfaction Survey Data Analysis 10 Statistical Inference for Causal Effects 173 Fabrizia Mealli, Barbara Pacini and Donald B. Rubin 10.1 Introduction to the potential outcome approach to causal inference 173 10.1.1 Causal inference primitives: Units, treatments, and potential outcomes 175 10.1.2 Learning about causal effects: Multiple units and the stable unit treatment value assumption 176 10.1.3 Defining causal estimands 177 10.2 Assignment mechanisms 179 10.2.1 The criticality of the assignment mechanism 179 10.2.2 Unconfounded and strongly ignorable assignment mechanisms 180 10.2.3 Confounded and ignorable assignment mechanisms 181 10.2.4 Randomized and observational studies 181 10.3 Inference in classical randomized experiments 182 10.3.1 Fisher’s approach and extensions 183 10.3.2 Neyman’s approach to randomization-based inference 183 10.3.3 Covariates, regression models, and Bayesian model-based inference 184 10.4 Inference in observational studies 185 10.4.1 Inference in regular designs 186 10.4.2 Designing observational studies: The role of the propensity score 186 10.4.3 Estimation methods 188 10.4.4 Inference in irregular designs 188 10.4.5 Sensitivity and bounds 189 10.4.6 Broken randomized experiments as templates for the analysis of some irregular designs 189 References 190 11 Bayesian Networks Applied to Customer Surveys 193 Ron S. Kenett, Giovanni Perruca and Silvia Salini 11.1 Introduction to Bayesian networks 193 11.2 The Bayesian network model in practice 197 11.2.1 Bayesian network analysis of the ABC 2010 ACSS 197 11.2.2 Transport data analysis 201 11.2.3 R packages and other software programs used for studying BNs 210 11.3 Prediction and explanation 211 11.4 Summary 213 References 213 12 Log-linear Model Methods 217 Stephen E. Fienberg and Daniel Manrique-Vallier 12.1 Introduction 217 12.2 Overview of log-linear models and methods 218 12.2.1 Two-way tables 218 12.2.2 Hierarchical log-linear models 220 12.2.3 Model search and selection 222 12.2.4 Sparseness in contingency tables and its implications 223 12.2.5 Computer programs for log-linear model analysis 223 12.3 Application to ABC survey data 224 12.4 Summary 227 References 228 13 CUB Models: Statistical Methods and Empirical Evidence 231 Maria Iannario and Domenico Piccolo 13.1 Introduction 231 13.2 Logical foundations and psychological motivations 233 13.3 A class of models for ordinal data 233 13.4 Main inferential issues 236 13.5 Specification of CUB models with subjects’ covariates 238 13.6 Interpreting the role of covariates 240 13.7 A more general sampling framework 241 13.7.1 Objects’ covariates 241 13.7.2 Contextual covariates 243 13.8 Applications of CUB models 244 13.8.1 Models for the ABC annual customer satisfaction survey 245 13.8.2 Students’ satisfaction with a university orientation service 246 13.9 Further generalizations 248 13.10 Concluding remarks 251 Acknowledgements 251 References 251 Appendix 255 A program in R for CUB models 255 A.1 Main structure of the program 255 A.2 Inference on CUB models 255 A.3 Output of CUB models estimation program 256 A.4 Visualization of several CUB models in the parameter space 257 A.5 Inference on CUB models in a multi-object framework 257 A.6 Advanced software support for CUB models 258 14 The Rasch Model 259 Francesca De Battisti, Giovanna Nicolini and Silvia Salini 14.1 An overview of the Rasch model 259 14.1.1 The origins and the properties of the model 259 14.1.2 Rasch model for hierarchical and longitudinal data 263 14.1.3 Rasch model applications in customer satisfaction surveys 265 14.2 The Rasch model in practice 267 14.2.1 Single model 267 14.2.2 Overall model 268 14.2.3 Dimension model 272 14.3 Rasch model software 277 14.4 Summary 278 References 279 15 Tree-based Methods and Decision Trees 283 Giuliano Galimberti and Gabriele Soffritti 15.1 An overview of tree-based methods and decision trees 283 15.1.1 The origins of tree-based methods 283 15.1.2 Tree graphs, tree-based methods and decision trees 284 15.1.3 CART 287 15.1.4 CHAID 293 15.1.5 PARTY 295 15.1.6 A comparison of CART, CHAID and PARTY 297 15.1.7 Missing values 297 15.1.8 Tree-based methods for applications in customer satisfaction surveys 298 15.2 Tree-based methods and decision trees in practice 300 15.2.1 ABC ACSS data analysis with tree-based methods 300 15.2.2 Packages and software implementing tree-based methods 303 15.3 Further developments 304 References 304 16 PLS Models 309 Giuseppe Boari and Gabriele Cantaluppi 16.1 Introduction 309 16.2 The general formulation of a structural equation model 310 16.2.1 The inner model 310 16.2.2 The outer model 312 16.3 The PLS algorithm 313 16.4 Statistical interpretation of PLS 319 16.5 Geometrical interpretation of PLS 320 16.6 Comparison of the properties of PLS and LISREL procedures 321 16.7 Available software for PLS estimation 323 16.8 Application to real data: Customer satisfaction analysis 323 References 329 17 Nonlinear Principal Component Analysis 333 Pier Alda Ferrari and Alessandro Barbiero 17.1 Introduction 333 17.2 Homogeneity analysis and nonlinear principal component analysis 334 17.2.1 Homogeneity analysis 334 17.2.2 Nonlinear principal component analysis 336 17.3 Analysis of customer satisfaction 338 17.3.1 The setting up of indicator 338 17.3.2 Additional analysis 340 17.4 Dealing with missing data 340 17.5 Nonlinear principal component analysis versus two competitors 343 17.6 Application to the ABC ACSS data 344 17.6.1 Data preparation 344 17.6.2 The homals package 345 17.6.3 Analysis on the ‘complete subset’ 346 17.6.4 Comparison of NLPCA with PCA and Rasch analysis 350 17.6.5 Analysis of ‘entire data set’ for the comparison of missing data treatments 352 17.7 Summary 355 References 355 18 Multidimensional Scaling 357 Nadia Solaro 18.1 An overview of multidimensional scaling techniques 357 18.1.1 The origins of MDS models 358 18.1.2 MDS input data 359 18.1.3 MDS models 362 18.1.4 Assessing the goodness of MDS solutions 369 18.1.5 Comparing two MDS solutions: Procrustes analysis 371 18.1.6 Robustness issues in the MDS framework 371 18.1.7 Handling missing values in MDS framework 373 18.1.8 MDS applications in customer satisfaction surveys 373 18.2 Multidimensional scaling in practice 374 18.2.1 Data sets analysed 375 18.2.2 MDS analyses of overall satisfaction with a set of ABC features: The complete data set 375 18.2.3 Weighting objects or items 381 18.2.4 Robustness analysis with the forward search 382 18.2.5 MDS analyses of overall satisfaction with a set of ABC features: The incomplete data set 383 18.2.6 Package and software for MDS methods 384 18.3 Multidimensional scaling in a future perspective 386 18.4 Summary 386 References 387 19 Multilevel Models for Ordinal Data 391 Leonardo Grilli and Carla Rampichini 19.1 Ordinal variables 391 19.2 Standard models for ordinal data 393 19.2.1 Cumulative models 394 19.2.2 Other models 395 19.3 Multilevel models for ordinal data 395 19.3.1 Representation as an underlying linear model with thresholds 396 19.3.2 Marginal versus conditional effects 397 19.3.3 Summarizing the cluster-level unobserved heterogeneity 397 19.3.4 Consequences of adding a covariate 398 19.3.5 Predicted probabilities 399 19.3.6 Cluster-level covariates and contextual effects 399 19.3.7 Estimation of model parameters 400 19.3.8 Inference on model parameters 401 19.3.9 Prediction of random effects 402 19.3.10 Software 403 19.4 Multilevel models for ordinal data in practice: An application to student ratings 404 References 408 20 Quality Standards and Control Charts Applied to Customer Surveys 413 Ron S. Kenett, Laura Deldossi and Diego Zappa 20.1 Quality standards and customer satisfaction 413 20.2 ISO 10004 guidelines for monitoring and measuring customer satisfaction 414 20.3 Control Charts and ISO 7870 417 20.4 Control charts and customer surveys: Standard assumptions 420 20.4.1 Introduction 420 20.4.2 Standard control charts 420 20.5 Control charts and customer surveys: Non-standard methods 426 20.5.1 Weights on counts: Another application of the c chart 426 20.5.2 The χ2 chart 427 20.5.3 Sequential probability ratio tests 428 20.5.4 Control chart over items: A non-standard application of SPC methods 429 20.5.5 Bayesian control chart for attributes: A modern application of SPC methods 432 20.5.6 Control chart for correlated Poisson counts: When things become fairly complicated 433 20.6 The M-test for assessing sample representation 433 20.7 Summary 435 References 436 21 Fuzzy Methods and Satisfaction Indices 439 Sergio Zani, Maria Adele Milioli and Isabella Morlini 21.1 Introduction 439 21.2 Basic definitions and operations 440 21.3 Fuzzy numbers 441 21.4 A criterion for fuzzy transformation of variables 443 21.5 Aggregation and weighting of variables 445 21.6 Application to the ABC customer satisfaction survey data 446 21.6.1 The input matrices 446 21.6.2 Main results 448 21.7 Summary 453 References 455 Appendix an Introduction to R 457 Stefano Maria Iacus A.1 Introduction 457 A.2 How to obtain R 457 A.3 Type rather than ‘point and click’ 458 A.3.1 The workspace 458 A.3.2 Graphics 458 A.3.3 Getting help 459 A.3.4 Installing packages 459 A.4 Objects 460 A.4.1 Assignments 460 A.4.2 Basic object types 462 A.4.3 Accessing objects and subsetting 466 A.4.4 Coercion between data types 469 A.5 S4 objects 470 A.6 Functions 472 A.7 Vectorization 473 A.8 Importing data from different sources 475 A.9 Interacting with databases 476 A.10 Simple graphics manipulation 477 A.11 Basic analysis of the ABC data 481 A.12 About this document 496 A.13 Bibliographical notes 496 References 496 Index 499

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Book SynopsisLatent Variable Models and Factor Analysis provides a comprehensive and unified approach to factor analysis and latent variable modeling from a statistical perspective. This book presents a general framework to enable the derivation of the commonly used models, along with updated numerical examples.Trade Review“Latent Variable Models and Factor Analysis provides a comprehensive and unified approach to factor analysis and latent variable modeling from a statistical perspective.” (Mathematical Reviews, 2012) "Statistical techniques to study the nature and interpretation of a latent variable should be highly useful for researchers and practitioners across several fields. The third edition of this book is comprehensive and provides a solid foundation for understanding these techniques, and is strongly recommended." (Book Pleasures, 2012)Table of ContentsPreface xi Acknowledgements xv 1 Basic Ideas and Examples 1 1.1 The statistical problem 1 1.2 The basic idea 3 1.3 Two Examples 4 1.4 A broader theoretical view 6 1.5 Illustration of an alternative approach 8 1.6 An overview of special cases 10 1.7 Principal components 11 1.8 The historical context 12 1.9 Closely related fields in Statistics 17 2 The General Linear Latent Variable Model 19 2.1 Introduction 19 2.2 The model 19 2.3 Some properties of the model 20 2.4 A special case 21 2.5 The sufficiency principle 22 2.6 Principal special cases 24 2.7 Latent variable models with non-linear terms 25 2.8 Fitting the models 27 2.9 Fitting by maximum likelihood 29 2.10 Fitting by Bayesian methods 30 2.11 Rotation 33 2.12 Interpretation 35 2.13 Sampling error of parameter estimates 38 2.14 The prior distribution 39 2.15 Posterior analysis 41 2.16 A further note on the prior 43 2.17 Psychometric Inference 44 3 The Normal Linear Factor Model 47 3.1 The model 47 3.2 Some distributional properties 48 3.3 Constraints on the model 50 3.4 Maximum likelihood estimation 50 3.5 Maximum likelihood estimation by the E-M algorithm 53 3.6 Sampling variation of estimators 55 3.7 Goodness of fit and choice of q 58 3.8 Fitting without normality assumptions: Least squares methods 59 3.9 Other methods of fitting 61 3.10 Approximate methods for estimating 62 3.11 Goodness-of-fit and choice of q for least squares methods 63 3.12 Further estimation issues 64 3.13 Rotation and related matters 69 3.14 Posterior analysis: The normal case 67 3.15 Posterior analysis: least squares 72 3.16 Posterior analysis: a reliability approach 74 3.17 Examples 74 4 Binary Data: Latent Trait Models 83 4.1 Preliminaries 83 4.2 The logit/normal model 84 4.3 The probit/normal model 86 4.4 The equivalence of the response function and underlying variable approaches 88 4.5 Fitting the logit/normal model: the E-M algorithm 90 4.6 Sampling properties of the maximum likelihood estimators 94 4.7 Approximate maximum likelihood estimators 95 4.8 Generalised least squares methods 96 4.9 Goodness of fit 97 4.10 Posterior analysis 100 4.11 Fitting the logit/normal and probit/normal models: Markov Chain Monte Carlo 102 4.12 Divergence of the estimation algorithm 109 4.13 Examples 109 5 Polytomous Data: Latent Trait Models 119 5.1 Introduction 119 5.2 A response function model based on the sufficiency principle 120 5.3 Parameter interpretation 124 5.4 Rotation 124 5.5 Maximum likelihood estimation of the polytomous logit model 125 5.6 An approximation to the likelihood 126 5.7 Binary data as a special case 134 5.8 Ordering of categories 136 5.9 An alternative underlying variable model 144 5.10 Posterior analysis 147 5.11 Further observations 148 5.12 Examples of the analysis of polytomous data using the logit model 149 6 Latent Class Models 157 6.1 Introduction 157 6.2 The latent class model with binary manifest variables 158 6.3 The latent class model for binary data as a latent trait model 159 6.4 Latent Classes within the GLLVM 161 6.5 Maximum likelihood estimation 162 6.6 Standard errors 164 6.7 Posterior analysis of the latent class model with binary manifest variables 166 6.8 Goodness of Fit 167 6.9 Examples for binary Data 167 6.10 Latent class models with unordered polytomous manifest variables 170 6.11 Latent class models with ordered polytomous manifest variables 171 6.12 Maximum likelihood estimation 172 6.13 Examples for unordered polytomous data 174 6.14 Identifiability 178 6.15 Starting values 180 6.16 Latent class models with metrical manifest variables 180 6.17 Models with ordered latent classes 181 6.18 Hybrid models 182 7 Models and Methods for Manifest Variables of Mixed Type 191 7.1 Introduction 191 7.2 Principal results 192 7.3 Other members of the exponential family 193 7.4 Maximum likelihood estimation 195 7.5 Sampling properties and Goodness of Fit 201 7.6 Mixed latent class models 202 7.7 Posterior analysis 203 7.8 Examples 204 7.9 Ordered categorical variables and other generalisations 208 8 Relationships Between Latent Variables 213 8.1 Scope 213 8.2 Correlated latent variables 213 8.3 Procrustes methods 215 8.4 Sources of prior knowledge 215 8.5 Linear structural relations models 216 8.6 The LISREL model 218 8.7 Adequacy of a structural equation model 221 8.8 Structural relationships in a general setting 222 8.9 Generalisations of the LISREL model 223 8.10 Examples of models which are indistinguishable 224 8.11 Implications for analysis 227 9 Related Techniques for Investigating Dependency 229 9.1 Introduction 229 9.2 Principal Components Analysis, (PCA) 229 9.3 An alternative to the normal factor model 236 9.4 Replacing latent variables by linear functions of the manifest variables 238 9.5 Estimation of correlations and regressions between latent variables 240 9.6 Q-Methodology 242 9.7 Concluding reflections of the role of latent variables in statistical modelling 244 References 247 Software appendix 247 References 249 Author Index 265 Subject Index 271

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Book SynopsisA practical guide for determining the evidential value of physicochemical data Microtraces of various materials (e.g. glass, paint, fibres, and petroleum products) are routinely subjected to physicochemical examination by forensic experts, whose role is to evaluate such physicochemical data in the context of the prosecution and defence propositions. Such examinations return various kinds of information, including quantitative data. From the forensic point of view, the most suitable way to evaluate evidence is the likelihood ratio. This book provides a collection of recent approaches to the determination of likelihood ratios and describes suitable software, with documentation and examples of their use in practice. The statistical computing and graphics software environment R, pre-computed Bayesian networks using Hugin Researcher and a new package, calcuLatoR, for the computation of likelihood ratios are all explored. Statistical Analysis in ForeTable of ContentsPreface xiii 1 Physicochemical data obtained in forensic science laboratories 1 1.1 Introduction 1 1.2 Glass 2 1.3 Flammable liquids: ATD-GC/MS technique 8 1.4 Car paints: Py-GC/MS technique 10 1.5 Fibres and inks: MSP-DAD technique 13 References 15 2 Evaluation of evidence in the form of physicochemical data 19 2.1 Introduction 19 2.2 Comparison problem 21 2.3 Classification problem 27 2.4 Likelihood ratio and Bayes’ theorem 31 References 32 3 Continuous data 35 3.1 Introduction 35 3.2 Data transformations 37 3.3 Descriptive statistics 39 3.4 Hypothesis testing 59 3.5 Analysis of variance 78 3.6 Cluster analysis 85 3.7 Dimensionality reduction 92 References 105 4 Likelihood ratio models for comparison problems 107 4.1 Introduction 107 4.2 Normal between-object distribution 108 4.3 Between-object distribution modelled by kernel density estimation 110 4.4 Examples 112 4.5 R Software 140 References 149 5 Likelihood ratio models for classification problems 151 5.1 Introduction 151 5.2 Normal between-object distribution 152 5.3 Between-object distribution modelled by kernel density estimation 155 5.4 Examples 157 5.5 R software 172 References 179 6 Performance of likelihood ratio methods 181 6.1 Introduction 181 6.2 Empirical measurement of the performance of likelihood ratios 182 6.3 Histograms and Tippett plots 183 6.4 Measuring discriminating power 186 6.5 Accuracy equals discriminating power plus calibration: Empirical cross-entropy plots 192 6.6 Comparison of the performance of different methods for LR computation 200 6.7 Conclusions: What to measure, and how 214 6.8 Software 215 References 216 Appendix A Probability 218 A.1 Laws of probability 218 A.2 Bayes’ theorem and the likelihood ratio 222 A.3 Probability distributions for discrete data 225 A.4 Probability distributions for continuous data 227 References 227 Appendix B Matrices: An introduction to matrix algebra 228 B.1 Multiplication by a constant 228 B.2 Adding matrices 229 B.3 Multiplying matrices 230 B.4 Matrix transposition 232 B.5 Determinant of a matrix 232 B.6 Matrix inversion 233 B.7 Matrix equations 235 B.8 Eigenvectors and eigenvalues 237 Reference 239 Appendix C Pool adjacent violators algorithm 240 References 243 Appendix D Introduction to R software 244 D.1 Becoming familiar with R 244 D.2 Basic mathematical operations in R 246 D.3 Data input 252 D.4 Functions in R 254 D.5 Dereferencing 255 D.6 Basic statistical functions 257 D.7 Graphics with R 258 D.8 Saving data 266 D.9 R codes used in Chapters 4 and 5 266 D.10 Evaluating the performance of LR models 289 Reference 293 Appendix E Bayesian network models 294 E.1 Introduction to Bayesian networks 294 E.2 Introduction to Hugin ResearcherTM software 296 References 308 Appendix F Introduction to calcuLatoR software 309 F.1 Introduction 309 F.2 Manual 309 Reference 314 Index 315

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Book SynopsisStatistics Analysis of Geographical Data: An Introduction provides a comprehensive and accessible introduction to the theory and practice of statistical analysis in geography.Table of ContentsPreface xi 1 Dealing with data 1 1.1 The role of statistics in geography 1 1.2 About this book 3 1.3 Data and measurement error 3 2 Collecting and summarizing data 13 2.1 Sampling methods 13 2.2 Graphicalsummaries 17 2.3 Summarizing data numerically 24 3 Probability and sampling distributions 37 3.1 Probability 37 3.2 Probability and the normal distribution: z]scores 39 3.3 Sampling distributions and the central limit theorem 43 4 Estimating parameters with confidence intervals 49 4.1 Confidence intervals on the mean of a normal distribution: the basics 49 4.2 Confidence intervals in practice: the t]distribution 50 4.3 Sample size 53 4.4 Confidence intervals for a proportion 53 5 Comparing datasets 55 5.1 Hypothesis testing with one sample: general principles 55 5.2 Comparing means from small samples: one]sample t]test 61 5.3 Comparing proportions for one sample 63 5.4 Comparing two samples 64 5.5 Non]parametric hypothesis testing 75 6 Comparing distributions: the Chi]squared test 81 6.1 Chi]squared test with one sample 81 6.2 Chi]squared test for two samples 84 7 Analysis of variance 89 7.1 Oneway analysis of variance 90 7.2 Assumptions and diagnostics 99 7.3 Multiple comparison tests after analysis of variance 101 7.4 Non]parametric methods in the analysis of variance 105 7.5 Summary and further applications 106 8 Correlation 109 8.1 Correlation analysis 109 8.2 Pearson’s product]moment correlation coefficient 110 8.3 Significance tests of correlation coefficient 112 8.4 Spearman’s rank correlation coefficient 114 8.5 Correlation and causality 116 9 Linear regression 121 9.1 Least]squares linear regression 121 9.2 Scatter plots 122 9.3 Choosing the line of best fit: the ‘least]squares’procedure 124 9.4 Analysis of residuals 128 9.5 Assumptions and caveats with regression 130 9.6 Is the regression significant? 131 9.7 Coefficient of determination 135 9.8 Confidence intervals and hypothesis tests concerning regression parameters 137 9.9 Reduced major axis regression 140 10 Spatial statistics 145 10.1 Spatial data 145 10.2 Summarizing spatial data 157 10.3 Identifying clusters 159 10.4 Interpolation and plotting contour maps 162 10.5 Spatial relationships 163 11 Time series analysis 173 11.1 Time series in geographical research 173 11.2 Analysing time series 174 Appendix A: Introduction to the R package 193 Appendix B: Statistical tables 205 References 241 Index 243

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Book SynopsisStatistics Analysis of Geographical Data: An Introduction provides a comprehensive and accessible introduction to the theory and practice of statistical analysis in geography.Table of ContentsPreface xi 1 Dealing with data 1 1.1 The role of statistics in geography 1 1.1.1 Why do geographers need to use statistics? 1 1.2 About this book 3 1.3 Data and measurement error 3 1.3.1 Types of geographical data: nominal, ordinal, interval, and ratio 3 1.3.2 Spatial data types 5 1.3.3 Measurement error, accuracy and precision 6 1.3.4 Reporting data and uncertainties 7 1.3.5 Significant figures 9 1.3.6 Scientific notation (standard form) 10 1.3.7 Calculations in scientific notation 11 Exercises 12 2 Collecting and summarizing data 13 2.1 Sampling methods 13 2.1.1 Research design 13 2.1.2 Random sampling 15 2.1.3 Systematic sampling 16 2.1.4 Stratified sampling 17 2.2 Graphical summaries 17 2.2.1 Frequency distributions and histograms 17 2.2.2 Time series plots 21 2.2.3 Scatter plots 22 2.3 Summarizing data numerically 24 2.3.1 Measures of central tendency: mean, median and mode 24 2.3.2 Mean 24 2.3.3 Median 25 2.3.4 Mode 25 2.3.5 Measures of dispersion 28 2.3.6 Variance 29 2.3.7 Standard deviation 30 2.3.8 Coefficient of variation 30 2.3.9 Skewness and kurtosis 33 Exercises 33 3 Probability and sampling distributions 37 3.1 Probability 37 3.1.1 Probability, statistics and random variables 37 3.1.2 The properties of the normal distribution 38 3.2 Probability and the normal distribution: z‐scores 39 3.3 Sampling distributions and the central limit theorem 43 Exercises 47 4 Estimating parameters with confidence intervals 49 4.1 Confidence intervals on the mean of a normal distribution: the basics 49 4.2 Confidence intervals in practice: the t‐distribution 50 4.3 Sample size 53 4.4 Confidence intervals for a proportion 53 Exercises 54 5 Comparing datasets 55 5.1 Hypothesis testing with one sample: general principles 55 5.1.1 Comparing means: one‐sample z‐test 56 5.1.2 p‐values 60 5.1.3 General procedure for hypothesis testing 61 5.2 Comparing means from small samples: one‐sample t‐test 61 5.3 Comparing proportions for one sample 63 5.4 Comparing two samples 64 5.4.1 Independent samples 64 5.4.2 Comparing means: t‐test with unknown population variances assumed equal 64 5.4.3 Comparing means: t‐test with unknown population variances assumed unequal 68 5.4.4 t‐test for use with paired samples (paired t‐test) 71 5.4.5 Comparing variances: F‐test 74 5.5 Non‐parametric hypothesis testing 75 5.5.1 Parametric and non‐parametric tests 75 5.5.2 Mann–whitney U‐test 75 Exercises 79 6 Comparing distributions: the Chi‐squared test 81 6.1 Chi‐squared test with one sample 81 6.2 Chi‐squared test for two samples 84 Exercises 87 7 Analysis of variance 89 7.1 One‐way analysis of variance 90 7.2 Assumptions and diagnostics 99 7.3 Multiple comparison tests after analysis of variance 101 7.4 Non‐parametric methods in the analysis of variance 105 7.5 Summary and further applications 106 Exercises 107 8 Correlation 109 8.1 Correlation analysis 109 8.2 Pearson’s product‐moment correlation coefficient 110 8.3 Significance tests of correlation coefficient 112 8.4 Spearman’s rank correlation coefficient 114 8.5 Correlation and causality 116 Exercises 117 9 Linear regression 121 9.1 Least‐squares linear regression 121 9.2 Scatter plots 122 9.3 Choosing the line of best fit: the ‘least‐squares’ procedure 124 9.4 Analysis of residuals 128 9.5 Assumptions and caveats with regression 130 9.6 Is the regression significant? 131 9.7 Coefficient of determination 135 9.8 Confidence intervals and hypothesis tests concerning regression parameters 137 9.8.1 Standard error of the regression parameters 137 9.8.2 Tests on the regression parameters 138 9.8.3 Confidence intervals on the regression parameters 139 9.8.4 Confidence interval about the regression line 140 9.9 Reduced major axis regression 140 9.10 Summary 142 Exercises 142 10 Spatial statistics 145 10.1 Spatial data 145 10.1.1 Types of spatial data 145 10.1.2 Spatial data structures 146 10.1.3 Map projections 149 10.2 Summarizing spatial data 157 10.2.1 Mean centre 157 10.2.2 Weighted mean centre 157 10.2.3 Density estimation 158 10.3 Identifying clusters 159 10.3.1 Quadrat test 159 10.3.2 Nearest neighbour statistics 162 10.4 Interpolation and plotting contour maps 162 10.5 Spatial relationships 163 10.5.1 Spatial autocorrelation 163 10.5.2 Join counts 164 Exercises 171 11 Time series analysis 173 11.1 Time series in geographical research 173 11.2 Analysing time series 174 11.2.1 Describing time series: definitions 174 11.2.2 Plotting time series 175 11.2.3 Decomposing time series: trends, seasonality and irregular fluctuations 179 11.2.4 Analysing trends 180 11.2.5 Removing trends (‘detrending’ data) 186 11.2.6 Quantifying seasonal variation 187 11.2.7 Autocorrelation 189 11.3 Summary 190 Exercises 190 Appendix A: Introduction to the R package 193 Appendix B: Statistical tables 205 References 241 Index 243

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Book SynopsisA guide to the validation and risk management of quantitative models used for pricing and hedging Whereas the majority of quantitative finance books focus on mathematics and risk management books focus on regulatory aspects, this book addresses the elements missed by this literature--the risks of the models themselves. This book starts from regulatory issues, but translates them into practical suggestions to reduce the likelihood of model losses, basing model risk and validation on market experience and on a wide range of real-world examples, with a high level of detail and precise operative indications.Table of ContentsPreface xi Acknowledgements xix Part I Theory and Practice of Model Risk Management 1 Understanding Model Risk 3 1.1 What Is Model Risk? 3 1.1.1 The Value Approach 4 1.1.2 The Price Approach 6 1.1.3 A Quant Story of the Crisis 9 1.1.4 A Synthetic View on Model Risk 17 1.2 Foundations of Modelling and the Reality of Markets 22 1.2.1 The Classic Framework 22 1.2.2 Uncertainty and Illiquidity 30 1.3 Accounting for Modellers 38 1.3.1 Fair Value 38 1.3.2 The Liquidity Bubble and the Accountancy Boards 40 1.3.3 Level 1, 2, 3 .go? 41 1.3.4 The Hidden Model Assumptions in ‘vanilla’ Derivatives 42 1.4 What Regulators Said After the Crisis 48 1.4.1 Basel New Principles: The Management Process 49 1.4.2 Basel New Principles: The Model, The Market and The Product 51 1.4.3 Basel New Principles: Operative Recommendations 52 1.5 Model Validation and Risk Management: Practical Steps 53 1.5.1 A Scheme for Model Validation 54 1.5.2 Special Points in Model Risk Management 59 1.5.3 The Importance of Understanding Models 60 2 Model Validation and Model Comparison: Case Studies 63 2.1 The Practical Steps of Model Comparison 63 2.2 First Example: The Models 65 2.2.1 The Credit Default Swap 66 2.2.2 Structural First-Passage Models 67 2.2.3 Reduced-Form Intensity Models 69 2.2.4 Structural vs Intensity: Information 72 2.3 First Example: The Payoff. Gap Risk in a Leveraged Note 74 2.4 The Initial Assessment 77 2.4.1 First Test: Calibration to Liquid Relevant Products 77 2.4.2 Second Test: a Minimum Level of Realism 78 2.5 The Core Risk in the Product 81 2.5.1 Structural Models: Negligible Gap Risk 82 2.5.2 Reduced-Form Models: Maximum Gap Risk 82 2.6 A Deeper Analysis: Market Consensus and Historical Evidence 85 2.6.1 What to Add to the Calibration Set 85 2.6.2 Performing Market Intelligence 86 2.6.3 The Lion and the Turtle. Incompleteness in Practice 86 2.6.4 Reality Check: Historical Evidence and Lack of it 87 2.7 Building a Parametric Family of Models 88 2.7.1 Understanding Model Implications 93 2.8 Managing Model Uncertainty: Reserves, Limits, Revisions 95 2.9 Model Comparison: Examples from Equity and Rates 99 2.9.1 Comparing Local and Stochastic Volatility Models in Pricing Equity Compound and Barrier Options 99 2.9.2 Comparing Short Rate and Market Models in Pricing Interest Rate Bermudan Options 105 3 Stress Testing and the Mistakes of the Crisis 111 3.1 Learning Stress Test from the Crisis 111 3.1.1 The Meaning of Stress Testing 112 3.1.2 Portfolio Stress Testing 113 3.1.3 Model Stress Testing 116 3.2 The Credit Market and the ‘Formula that Killed Wall Street’ 118 3.2.1 The CDO Payoff 118 3.2.2 The Copula 119 3.2.3 Applying the Copula to CDOs 122 3.2.4 The Market Quotation Standard 124 3.3 Portfolio Stress Testing and the Correlation Mistake 125 3.3.1 From Flat Correlation Towards a Realistic Approach 126 3.3.2 A Correlation Parameterization to Stress the Market Skew 131 3.4 Payoff Stress and the Liquidity Mistake 136 3.4.1 Detecting the Problem: Losses Concentrated in Time 137 3.4.2 The Problem in Practice 139 3.4.3 A Solution. From Copulas to Real Models 145 3.4.4 Conclusions 150 3.5 Testing with Historical Scenarios and the Concentration Mistake 151 3.5.1 The Mapping Methods for Bespoke Portfolios 152 3.5.2 The Lehman Test 156 3.5.3 Historical Scenarios to Test Mapping Methods 157 3.5.4 The Limits of Mapping and the Management of Model Risk 164 3.5.5 Conclusions 168 4 Preparing for Model Change. Rates and Funding in the New Era 171 4.1 Explaining the Puzzle in the Interest Rates Market and Models 171 4.1.1 The Death of a Market Model: 9 August 2007 173 4.1.2 Finding the New Market Model 174 4.1.3 The Classic Risk-free Market Model 178 4.1.4 A Market Model with Stable Default Risk 182 4.1.5 A Market with Volatile Credit Risk 192 4.1.6 Conclusions 200 4.2 Rethinking the Value of Money: The Effect of Liquidity in Pricing 201 4.2.1 The Setting 204 4.2.2 Standard DVA: Is Something Missing? 206 4.2.3 Standard DVA plus Liquidity: Is Something Duplicated? 207 4.2.4 Solving the Puzzle 207 4.2.5 Risky Funding for the Borrower 208 4.2.6 Risky Funding for the Lender and the Conditions for Market Agreement 209 4.2.7 Positive Recovery Extension 210 4.2.8 Two Ways of Looking at the Problem: Default Risk or Funding Benefit? The Accountant vs the Salesman 211 4.2.9 Which Direction for Future Pricing? 214 Part II Snakes in the Grass: Where Model Risk Hides 5 Hedging 219 5.1 Model Risk and Hedging 219 5.2 Hedging and Model Validation: What is Explained by P&L Explain? 221 5.2.1 The Sceptical View 222 5.2.2 The Fundamentalist View and Black and Scholes 222 5.2.3 Back to Reality 224 5.2.4 Remarks: Recalibration, Hedges and Model Instability 226 5.2.5 Conclusions: from Black and Scholes to Real Hedging 228 5.3 From Theory to Practice: Real Hedging 229 5.3.1 Stochastic Volatility Models: SABR 231 5.3.2 Test Hedging Behaviour Leaving Nothing Out 232 5.3.3 Real Hedging for Local Volatility Models 238 5.3.4 Conclusions: the Reality of Hedging Strategies 241 6 Approximations 243 6.1 Validate and Monitor the Risk of Approximations 243 6.2 The Swaption Approximation in the Libor Market Model 245 6.2.1 The Three Technical Problems in Interest Rate Modelling 245 6.2.2 The Libor Market Model and the Swaption Market 247 6.2.3 Pricing Swaptions 250 6.2.4 Understanding and Deriving the Approximation 253 6.2.5 Testing the Approximation 257 6.3 Approximations for CMS and the Shape of the Term Structure 264 6.3.1 The CMS Payoff 265 6.3.2 Understanding Convexity Adjustments 266 6.3.3 The Market Approximation for Convexity Adjustments 267 6.3.4 A General LMM Approximation 269 6.3.5 Comparing and Testing the Approximations 271 6.4 Testing Approximations Against Exact. Dupire’s Idea 276 6.4.1 Perfect Positive Correlation 278 6.4.2 Perfect Negative Correlation 280 6.5 Exercises on Risk in Computational Methods 283 6.5.1 Approximation 283 6.5.2 Integration 285 6.5.3 Monte Carlo 285 7 Extrapolations 287 7.1 Using the Market to Complete Information: Asymptotic Smile 288 7.1.1 The Indetermination in the Asymptotic Smile 288 7.1.2 Pricing CMS with a Smile: Extrapolating to Infinity 292 7.1.3 Using CMS Information to Transform Extrapolation into Interpolation and Fix the Indetermination 293 7.2 Using Mathematics to Complete Information: Correlation Skew 295 7.2.1 The Expected Tranched Loss 295 7.2.2 Properties for Interpolation 298 7.2.3 Properties for Turning Extrapolation into Interpolation 298 8 Correlations 303 8.1 The Technical Difficulties in Computing Correlations 303 8.1.1 Correlations in Interest Rate Modelling 305 8.1.2 Cross-currency Correlations 307 8.1.3 Stochastic Volatility Correlations 312 8.2 Fundamental Errors in Modelling Correlations 315 8.2.1 The Zero-correlation Error 316 8.2.2 The 1-Correlation Error 319 9 Calibration 323 9.1 Calibrating to Caps/Swaptions and Pricing Bermudans 324 9.1.1 Calibrating Caplets 325 9.1.2 Understanding the Term Structure of Volatility 326 9.1.3 Different Parameterizations 329 9.1.4 The Evolution of the Term Structure of Volatility 332 9.1.5 The Effect on Early-Exercise Derivatives 334 9.1.6 Reducing Our Indetermination in Pricing Bermudans: Liquid European Swaptions 335 9.2 The Evolution of the Forward Smiles 340 10 When the Payoff is Wrong 347 10.1 The Link Between Model Errors and Payoff Errors 347 10.2 The Right Payoff at Default: The Impact of the Closeout Convention 348 10.2.1 How Much Will be Paid at Closeout, Really? 350 10.2.2 What the Market Says and What the ISDA Says 352 10.2.3 A Quantitative Analysis of the Closeout 353 10.2.4 A Summary of the Findings and Some Conclusions on Payoff Uncertainty 360 10.3 Mathematical Errors in the Payoff of Index Options 362 10.3.1 Too Much Left Out 364 10.3.2 Too Much Left In 365 10.3.3 Empirical Results with the Armageddon Formula 365 10.3.4 Payoff Errors and Armageddon Probability 367 11 Model Arbitrage 371 11.1 Introduction 371 11.2 Capital Structure Arbitrage 373 11.2.1 The Credit Model 373 11.2.2 The Equity Model 375 11.2.3 From Barrier Options to Equity Pricing 377 11.2.4 Capital-structure Arbitrage and Uncertainty 381 11.3 The Cap-Swaption Arbitrage 391 11.4 Conclusion: Can We Use No-Arbitrage Models to Make Arbitrage? 394 12 Appendix 397 12.1 Random Variables 397 12.1.1 Generating Variables from Uniform Draws 397 12.1.2 Copulas 397 12.1.3 Normal and Lognormal 398 12.2 Stochastic Processes 399 12.2.1 The Law of Iterated Expectation 399 12.2.2 Diffusions, Brownian Motions and Martingales 400 12.2.3 Poisson Process 403 12.2.4 Time-dependent Intensity 404 12.3 Useful Results from Quantitative Finance 405 12.3.1 Black and Scholes (1973) and Black (1976) 405 12.3.2 Change of Numeraire 407 Bibliography 409 Index 417

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Book SynopsisThis is the only major text in the area of chemometrics published over the last decade focusing exclusively on pattern recognition. The coverage uses real world pattern recognition case studies, often involving quite large and complex datasets.Table of ContentsAcknowledgements. Preface. 1 Introduction. 1.1 Past, Present and Future. 1.2 About this Book. Bibliography. 2 Case Studies. 2.1 Introduction. 2.2 Datasets, Matrices and Vectors. 2.3 Case Study 1: Forensic Analysis of Banknotes. 2.4 Case Study 2: Near Infrared Spectroscopic Analysis of Food. 2.5 Case Study 3: Thermal Analysis of Polymers. 2.6 Case Study 4: Environmental Pollution using Headspace Mass Spectrometry. 2.7 Case Study 5: Human Sweat Analysed by Gas Chromatography Mass Spectrometry. 2.8 Case Study 6: Liquid Chromatography Mass Spectrometry of Pharmaceutical Tablets. 2.9 Case Study 7: Atomic Spectroscopy for the Study of Hypertension. 2.10 Case Study 8: Metabolic Profiling of Mouse Urine by Gas Chromatography of Urine Extracts. 2.11 Case Study 9: Nuclear Magnetic Resonance Spectroscopy for Salival Analysis of the Effect of Mouthwash. 2.12 Case Study 10: Simulations. 2.13 Case Study 11: Null Dataset. 2.14 Case Study 12: GCMS and Microbiology of Mouse Scent Marks. Bibliography. 3 Exploratory Data Analysis. 3.1 Introduction. 3.2 Principal Components Analysis. 3.2.1 Background. 3.2.2 Scores and Loadings. 3.2.3 Eigenvalues. 3.2.4 PCA Algorithm. 3.2.5 Graphical Representation. 3.3 Dissimilarity Indices, Principal Co-ordinates Analysis and Ranking. 3.3.1 Dissimilarity. 3.3.2 Principal Co-ordinates Analysis. 3.3.3 Ranking. 3.4 Self Organizing Maps. 3.4.1 Background. 3.4.2 SOM Algorithm. 3.4.3 Initialization. 3.4.4 Training. 3.4.5 Map Quality. 3.4.6 Visualization. Bibliography. 4 Preprocessing. 4.1 Introduction. 4.2 Data Scaling. 4.2.1 Transforming Individual Elements. 4.2.2 Row Scaling. 4.2.3 Column Scaling. 4.3 Multivariate Methods of Data Reduction. 4.3.1 Largest Principal Components. 4.3.2 Discriminatory Principal Components. 4.3.3 Partial Least Squares Discriminatory Analysis Scores. 4.4 Strategies for Data Preprocessing. 4.4.1 Flow Charts. 4.4.2 Level 1. 4.4.3 Level 2. 4.4.4 Level 3. 4.4.5 Level 4. Bibliography. 5 Two Class Classifiers. 5.1 Introduction. 5.1.1 Two Class Classifiers. 5.1.2 Preprocessing. 5.1.3 Notation. 5.1.4 Autoprediction and Class Boundaries. 5.2 Euclidean Distance to Centroids. 5.3 Linear Discriminant Analysis. 5.4 Quadratic Discriminant Analysis. 5.5 Partial Least Squares Discriminant Analysis. 5.5.1 PLS Method. 5.5.2 PLS Algorithm. 5.5.3 PLS-DA. 5.6 Learning Vector Quantization. 5.6.1 Voronoi Tesselation and Codebooks. 5.6.2 LVQ1. 5.6.3 LVQ3. 5.6.4 LVQ Illustration and Summary of Parameters. 5.7 Support Vector Machines. 5.7.1 Linear Learning Machines. 5.7.2 Kernels. 5.7.3 Controlling Complexity and Soft Margin SVMs. 5.7.4 SVM Parameters. Bibliography. 6 One Class Classifiers. 6.1 Introduction. 6.2 Distance Based Classifiers. 6.3 PC Based Models and SIMCA. 6.4 Indicators of Significance. 6.4.1 Gaussian Density Estimators and Chi-Squared. 6.4.2 Hotelling’s T2. 6.4.3 D-Statistic. 6.4.4 Q-Statistic or Squared Prediction Error. 6.4.5 Visualization of D- and Q-Statistics for Disjoint PC Models. 6.4.6 Multivariate Normality and What to do if it Fails. 6.5 Support Vector Data Description. 6.6 Summarizing One Class Classifiers. 6.6.1 Class Membership Plots. 6.6.2 ROC Curves. Bibliography. 7 Multiclass Classifiers. 7.1 Introduction. 7.2 EDC, LDA and QDA. 7.3 LVQ. 7.4 PLS. 7.4.1 PLS2. 7.4.2 PLS1. 7.5 SVM. 7.6 One against One Decisions. Bibliography. 8 Validation and Optimization. 8.1 Introduction. 8.1.1 Validation. 8.1.2 Optimization. 8.2 Classification Abilities, Contingency Tables and Related Concepts. 8.2.1 Two Class Classifiers. 8.2.2 Multiclass Classifiers. 8.2.3 One Class Classifiers. 8.3 Validation. 8.3.1 Testing Models. 8.3.2 Test and Training Sets. 8.3.3 Predictions. 8.3.4 Increasing the Number of Variables for the Classifier. 8.4 Iterative Approaches for Validation. 8.4.1 Predictive Ability, Model Stability, Classification by Majority Vote and Cross Classification Rate. 8.4.2 Number of Iterations. 8.4.3 Test and Training Set Boundaries. 8.5 Optimizing PLS Models. 8.5.1 Number of Components: Cross-Validation and Bootstrap. 8.5.2 Thresholds and ROC Curves. 8.6 Optimizing Learning Vector Quantization Models. 8.7 Optimizing Support Vector Machine Models. Bibliography. 9 Determining Potential Discriminatory Variables. 9.1 Introduction. 9.1.1 Two Class Distributions. 9.1.2 Multiclass Distributions. 9.1.3 Multilevel and Multiway Distributions. 9.1.4 Sample Sizes. 9.1.5 Modelling after Variable Reduction. 9.1.6 Preliminary Variable Reduction. 9.2 Which Variables are most Significant?. 9.2.1 Basic Concepts: Statistical Indicators and Rank. 9.2.2 T-Statistic and Fisher Weights. 9.2.3 Multiple Linear Regression, ANOVA and the F-Ratio. 9.2.4 Partial Least Squares. 9.2.5 Relationship between the Indicator Functions. 9.3 How Many Variables are Significant? 9.3.1 Probabilistic Approaches. 9.3.2 Empirical Methods: Monte Carlo. 9.3.3 Cost/Benefit of Increasing the Number of Variables. Bibliography. 10 Bayesian Methods and Unequal Class Sizes. 10.1 Introduction. 10.2 Contingency Tables and Bayes’ Theorem. 10.3 Bayesian Extensions to Classifiers. Bibliography. 11 Class Separation Indices. 11.1 Introduction. 11.2 Davies Bouldin Index. 11.3 Silhouette Width and Modified Silhouette Width. 11.3.1 Silhouette Width. 11.3.2 Modified Silhouette Width. 11.4 Overlap Coefficient. Bibliography. 12 Comparing Different Patterns. 12.1 Introduction. 12.2 Correlation Based Methods. 12.2.1 Mantel Test. 12.2.2 RV Coefficient. 12.3 Consensus PCA. 12.4 Procrustes Analysis. Bibliography. Index.

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Book SynopsisFinite mixture models are typically used where the population being studied is heterogeneous in composition. This work aims to offer an up-to-date account of the major issues involved with finite modelling. There is a practical emphasis on the applications of mixture models.Trade Review"This is an excellent book.... I enjoyed reading this book. I recommend it highly to both mathematical and applied statisticians." (Technometrics, February 2002) "This book will become popular to many researchers...the material covered is so wide that it will make this book a standard reference for the forthcoming years." (Zentralblatt MATH, Vol. 963, 2001/13) "the material covered is so wide that it will make this book a standard reference for the forthcoming years." (Zentralblatt MATH, Vol.963, No.13, 2001) "This book is excellent reading...should also serve as an excellent handbook on mixture modelling..." (Mathematical Reviews, 2002b) "...contains valuable information about mixtures for researchers..." (Journal of Mathematical Psychology, 2002) "...a masterly overview of the area...It is difficult to ask for more and there is no doubt that McLachlan and Peel's book will be the standard reference on mixture models for many years to come." (Statistical Methods in Medical Research, Vol. 11, 2002) "...they are to be congratulated on the extent of their achievement..." (The Statistician, Vol.51, No.3)Table of ContentsGeneral Introduction. ML Fitting of Mixture Models. Multivariate Normal Mixtures. Bayesian Approach to Mixture Analysis. Mixtures with Nonnormal Components. Assessing the Number of Components in Mixture Models. Multivariate t Mixtures. Mixtures of Factor Analyzers. Fitting Mixture Models to Binned Data. Mixture Models for Failure-Time Data. Mixture Analysis of Directional Data. Variants of the EM Algorithm for Large Databases. Hidden Markov Models. Appendices. References. Indexes.

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Book SynopsisAn accessible book on sampling techniques with emphasis on and illustrations from surveys of human populations. Explains how to design and execute valid samples of moderate dimensions and difficulty, avoid selection biases and how to become more adept at evaluating sample results, judge their validity and limits of inference, applicability and precision. Contains numerous practical procedures, the domestic arts of sampling along with its science plus invaluable tricks that are usually learned only in apprenticeship.Table of ContentsFUNDAMENTALS OF SURVEY SAMPLING. Basic Concepts of Sampling. Stratified Sampling. Systematic Sampling; Stratification Techniques. Cluster Sampling and Subsampling. Unequal Clusters. Selection with Probabilities Proportional to Size Measures(PPS). The Economic Design of Surveys. SPECIAL PROBLEMS AND TECHNIQUES. Area Sampling. Multistage Sampling. Sampling from Imperfect Frames. Some Selection Techniques. RELATED CONCEPTS. Biases and Nonsampling Errors. Some Issues of Inference from Survey Data. Appendices. References. Answers to Selected Problems. Index.

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Book SynopsisThis book contains material on compound Poisson random variables including an identity which can be used to efficiently compute moments, Poisson approximations, and coverage of the mean time spent in transient states as well as examples relating to the Gibba s sampler, the Metropolis algorithm and mean cover time in star graphs.Table of ContentsPreliminaries. The Poisson Process. Renewal Theory. Markov Chains. Continuous-Time Markov Chains. Martingales. Random Walks. Brownian Motion and Other Markov Processes. Stochastic Order Relations. Poisson Approximations. Answers and Solutions to Selected Problems. Index.

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Book SynopsisChemometrics encompasses a variety of statistical tools used to effectively design, analyze and interpret experimental data. The field has evolved rapidly over the last several years due to the widespread availability of powerful, inexpensive computers and available software packages.Trade Review"...probably the best introductory text that I have read on the subject...I would recommend this book for an introductory course...whithout the slightest hesitation." (Microchemical Journal, Vol. 69, 2001)Table of ContentsThe Six Habits of an Effective Chemometrician. Defining the Problem. Preprocessing. Pattern Recognition. Multivariate Calibration and Prediction. References. Index.

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