Probability and statistics Books

Book SynopsisOf related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts . an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models. highly recommend[ed].Table of ContentsLinear Regression Analysis. Constructing and Checking the Model. Least Squares Regression. Least Absolute Deviations Regression. M-Regression. Nonparametric Regression. Bayesian Regression. Ridge Regression. Comparisons. Other Methods.

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Book SynopsisOriginally published in 1958, this text offers a simple analysis of the principles of experimental design. Emphasis is placed on basic concepts rather than the calculation of technical details. It is possible to use the book in conjunction with a text on statistical analysis.Table of ContentsPreliminaries. Some Key Assumptions. Designs for the Reduction of Error. Use of Supplementary Observations to Reduce Error. Randomization. Basic Ideas About Factorial Experiments. Design of Simple Factorial Experiments. Choice of Number of Observations. Choice of Units, Treatments, and Observations. More About Latin Squares. Incomplete Nonfactorial Designs. Fractional Replication and Confounding. Cross-Over Designs. Some Special Problems. General Bibliography. Appendix. Indexes.

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Book SynopsisSequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved.Table of ContentsPreliminaries. Sums of Independent Random Variables. Optimal Stopping. Reduction to a Single Dimension. Accessibility and Filtration Structure. Sequential Sampling. Optimal Sequential Control. Multiarmed Bandits. The Markovian Case. Optimal Switching Between Two Random Walks. Bibliography. Indexes.

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Book SynopsisThe definitive reference for statistical distributions Continuous Univariate Distributions, Volume 1 offers comprehensive guidance toward the most commonly used statistical distributions, including normal, lognormal, inverse Gaussian, Pareto, Cauchy, gamma distributions and more. Each distribution includes clear definitions and properties, plus methods of inference, applications, algorithms, characterizations, and reference to other related distributions. Organized for easy navigation and quick reference, this book is an invaluable resource for investors, data analysts, or anyone working with statistical distributions on a regular basis.Table of ContentsContinuous Distributions (General). Normal Distributions. Lognormal Distributions. Inverse Gaussian (Wald) Distributions. Cauchy Distribution. Gamma Distributions. Chi-Square Distributions Including Chi and Rayleigh. Exponential Distributions. Pareto Distributions. Weibull Distributions. Abbreviations. Indexes.

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Book SynopsisConsists of invited papers, from internationally recognized researchers, chosen for their quality as well as their overall unity. Describes current methods along with innovative research and presents new technologies for solving problems unique to establishment surveys.Table of ContentsPartial table of contents: FRAMES AND BUSINESS REGISTERS. Defining and Classifying Statistical Units (S. Nijhowne). Changes in Populations of Statistical Units (P. Struijs & A.Willeboordse). SAMPLE DESIGN AND SELECTION. Coordination of Samples Using Permanent Random Numbers (E.Ohlsson). Business Surveys as a Network Sample (A. Johnson). DATA COLLECTION AND RESPONSE QUALITY. Designing the Data Collection Process (C. Dippo, et al.). Electronic Data Interchange (C. Ambler, et al.). DATA PROCESSING. Matching and Record Linkage (W. Winkler). Protecting Confidentiality in Business Surveys (L. Cox). WEIGHTING AND ESTIMATION. Outliers in Business Surveys (H. Lee). Combining Design-Based and Model-Based Inference (K. Brewer). PAST, PRESENT, AND FUTURE DIRECTIONS. Quality Assurance for Business Surveys (G. Griffiths & S.Linacre). Business Surveys in Ten Years' Time (J. Ryten). Index.

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Book SynopsisReflecting emerging principles and trends, Measurement Errors in Surveys documents the current state of measurement errors in surveys; reports new research findings; and promotes interdisciplinary exchanges in numerous approaches in assessing, modeling and reducing measurement inaccuracies in surveys.Table of ContentsPreface. Introduction (W. Kruskal). 1. Measurement Error Across Disciplines (R. Groves). SECTION A: THE QUESTIONAIRE. 2. The Current Status of Questionnaire Design (N. Bradburn & S. Sudman). 3. Response Alternatives: The Impact of Their Choice and Presentation Order (N. Schwarz & H. Hippler). 4. Context Effects in the General Social Survey (T. Smith). 5. Mode Effects of Cognitively Designed Recall Questions: A Comparison of Answers to Telephone and Mail Surveys (D. Dillman & J. Tarnai). 6. Nonexperimental Research on Question Wording Effects: A Contribution to Solving the Generalizability Problem (N. Molenaar). 7. Measurement Errors in Business Surveys (S. Dutka & L. Frankel). SECTION B: RESPONDENTS AND RESPONSES. 8. Recall Error: Sources and Bias Reduction Techniques (D. Eisenhower, et al.). 9. Measurement Effects in Self vs. Proxy Response to Survey Questions: An Information-Processing Perspective (J. Blair, et al.). 10. An Alternative Approach to Obtaining Personal History Data (B. Means, et al.). 11. The Item Count Technique as a Method of Indirect Questioning: A Review of Its Development and a Case Study Application (J. Droitcour, et al.). 12. Toward a Response Model in Establishment Surveys (W. Edwards & D. Cantor). SECTION C: INTERVIEWERS AND OTHER MEANS OF DATA COLLECTION. 13. Data Collection Methods and Measurement Error: An Overview (L. Lyberg & D. Kasprzyk). 14. Reducing Inte5rviewer-Related Error Through Interviewer Training, Supervision, and Other Means (F. Fowler). 15. The Design and Analysis of Reinterview: An Overview (G. Forsman & I. Schreiner). 16. Expenditure Diary Surveys and Their Associated Errors (A. Silberstein & S. Scott). 17. A Review of Errors of Direct Observation in Crop Yield Surveys (R. Fecso). 18. Measurement Error in Continuing Surveys of the Grocery Retail Trade Using Electronic Data Collection Methods (J. Donmyer, et al.). SECTION D: MEASUREMENT ERRORS IN THE INTERVIEW PROCESS. 19. Conversation with a Purpose—or Conversation? Interaction in the Standardized Interview (N. Schaeffer). 20. Cognitive Laboratory Methods: A Taxonomy (B. Forsyth & J. Lessler). 21. Studying Respondent-Interviewer Interaction: The Relationship Between Interviewing Style, Interviewer Behavior, and Response Behavior (J. van der Zouwen, et al.). 22. The Effect of Interviewer and Respondent Characteristics on the Quality of Survey Data: A Multilevel Model (J. Hox, et al.). 23. Interviewer, Respondent, and Regional Office Effects on Response Variance: A Statistical Decomposition (D. Hill). SECTION E: MODELING MEASUREMENT ERRORS AND THEIR EFFECTS ON ESTIMATION AND DATA ANALYSIS. 24. Approaches to the Modeling of Measurement Errors (P. Biemer & L. Stokes). 25. A Mixed Model for Analyzing Measurement Errors for Dichotomous Variables (J. Pannekoek). 26. Models for Memory Effects in Count Data (P. van Dosselaar). 27. Simple Response Variance: Estimation and Determinants (C. O'Muircheartaigh). 28. Evaluation of Measurement Instruments Using a Structural Modeling Approach (W. Saris & F. Andrews). 29. A Path Analysis of Cross-National Data Taking Measurement Errors Into Account (I. Munck). 30. Regression Estimation in the Presence of Measurement Error (W. Fuller). 31. Chi-Squared Tests with Complex Survey Data Subject to Misclassification Error (J. Rao & D. Thomas). 32. The Effect of Measurement Error on Event History Analysis (D. Holt, et al.). References. Index.

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Book SynopsisClarifies modern data analysis through nonparametric density estimation for a complete working knowledge of the theory and methods Featuring a thoroughly revised presentation, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition maintains an intuitive approach to the underlying methodology and supporting theory of density estimation. Including new material and updated research in each chapter, the Second Edition presents additional clarification of theoretical opportunities, new algorithms, and up-to-date coverage of the unique challenges presented in the field of data analysis. The new edition focuses on the various density estimation techniques and methods that can be used in the field of big data. Defining optimal nonparametric estimators, the Second Edition demonstrates the density estimation tools to use when dealing with various multivariate structures in univariate, bivariate, trivariate, and quadrivariate data analyTrade Review"The book is an ideal reference for theoretical and applied statisticians, practicing engineers, as well as readers interested in the theoretical aspects of nonparametric estimation and the application of these methods to multivariate data. The second edition is also useful as a textbook for introductory courses in kernel statistics, smoothing, advanced computational statistics, and general forms of statistical distributions." (Zentralblatt MATH, 1 June 2015)Table of ContentsPREFACE TO SECOND EDITION xv PREFACE TO FIRST EDITION xvii 1 Representation and Geometry of Multivariate Data 1 1.1 Introduction 1 1.2 Historical Perspective 4 1.3 Graphical Display of Multivariate Data Points 5 1.3.1 Multivariate Scatter Diagrams 5 1.3.2 Chernoff Faces 11 1.3.3 Andrews’ Curves and Parallel Coordinate Curves 12 1.3.4 Limitations 14 1.4 Graphical Display of Multivariate Functionals 16 1.4.1 Scatterplot Smoothing by Density Function 16 1.4.2 Scatterplot Smoothing by Regression Function 18 1.4.3 Visualization of Multivariate Functions 19 1.4.3.1 Visualizing Multivariate Regression Functions 24 1.4.4 Overview of Contouring and Surface Display 26 1.5 Geometry of Higher Dimensions 28 1.5.1 Polar Coordinates in d Dimensions 28 1.5.2 Content of Hypersphere 29 1.5.3 Some Interesting Consequences 30 1.5.3.1 Sphere Inscribed in Hypercube 30 1.5.3.2 Hypervolume of a Thin Shell 30 1.5.3.3 Tail Probabilities of Multivariate Normal 31 1.5.3.4 Diagonals in Hyperspace 31 1.5.3.5 Data Aggregate Around Shell 32 1.5.3.6 Nearest Neighbor Distances 32 Problems 33 2 Nonparametric Estimation Criteria 36 2.1 Estimation of the Cumulative Distribution Function 37 2.2 Direct Nonparametric Estimation of the Density 39 2.3 Error Criteria for Density Estimates 40 2.3.1 MISE for Parametric Estimators 42 2.3.1.1 Uniform Density Example 42 2.3.1.2 General Parametric MISE Method with Gaussian Application 43 2.3.2 The L1 Criterion 44 2.3.2.1 L1 versus L2 44 2.3.2.2 Three Useful Properties of the L1 Criterion 44 2.3.3 Data-Based Parametric Estimation Criteria 46 2.4 Nonparametric Families of Distributions 48 2.4.1 Pearson Family of Distributions 48 2.4.2 When Is an Estimator Nonparametric? 49 Problems 50 3 Histograms: Theory and Practice 51 3.1 Sturges’ Rule for Histogram Bin-Width Selection 51 3.2 The L2 Theory of Univariate Histograms 53 3.2.1 Pointwise Mean Squared Error and Consistency 53 3.2.2 Global L2 Histogram Error 56 3.2.3 Normal Density Reference Rule 59 3.2.3.1 Comparison of Bandwidth Rules 59 3.2.3.2 Adjustments for Skewness and Kurtosis 60 3.2.4 Equivalent Sample Sizes 62 3.2.5 Sensitivity of MISE to Bin Width 63 3.2.5.1 Asymptotic Case 63 3.2.5.2 Large-Sample and Small-Sample Simulations 64 3.2.6 Exact MISE versus Asymptotic MISE 65 3.2.6.1 Normal Density 66 3.2.6.2 Lognormal Density 68 3.2.7 Influence of Bin Edge Location on MISE 69 3.2.7.1 General Case 69 3.2.7.2 Boundary Discontinuities in the Density 69 3.2.8 Optimally Adaptive Histogram Meshes 70 3.2.8.1 Bounds on MISE Improvement for Adaptive Histograms 71 3.2.8.2 Some Optimal Meshes 72 3.2.8.3 Null Space of Adaptive Densities 72 3.2.8.4 Percentile Meshes or Adaptive Histograms with Equal Bin Counts 73 3.2.8.5 Using Adaptive Meshes versus Transformation 74 3.2.8.6 Remarks 75 3.3 Practical Data-Based Bin Width Rules 76 3.3.1 Oversmoothed Bin Widths 76 3.3.1.1 Lower Bounds on the Number of Bins 76 3.3.1.2 Upper Bounds on Bin Widths 78 3.3.2 Biased and Unbiased CV 79 3.3.2.1 Biased CV 79 3.3.2.2 Unbiased CV 80 3.3.2.3 End Problems with BCV and UCV 81 3.3.2.4 Applications 81 3.4 L2 Theory for Multivariate Histograms 83 3.4.1 Curse of Dimensionality 85 3.4.2 A Special Case: d = 2 with Nonzero Correlation 87 3.4.3 Optimal Regular Bivariate Meshes 88 3.5 Modes and Bumps in a Histogram 89 3.5.1 Properties of Histogram “Modes” 91 3.5.2 Noise in Optimal Histograms 92 3.5.3 Optimal Histogram Bandwidths for Modes 93 3.5.4 A Useful Bimodal Mixture Density 95 3.6 Other Error Criteria: L1,L4,L6,L8, and L∞ 96 3.6.1 Optimal L1 Histograms 96 3.6.2 Other LP Criteria 97 Problems 97 4 Frequency Polygons 100 4.1 Univariate Frequency Polygons 101 4.1.1 Mean Integrated Squared Error 101 4.1.2 Practical FP Bin Width Rules 104 4.1.3 Optimally Adaptive Meshes 107 4.1.4 Modes and Bumps in a Frequency Polygon 109 4.2 Multivariate Frequency Polygons 110 4.3 Bin Edge Problems 113 4.4 Other Modifications of Histograms 114 4.4.1 Bin Count Adjustments 114 4.4.1.1 Linear Binning 114 4.4.1.2 Adjusting FP Bin Counts to Match Histogram Areas 117 4.4.2 Polynomial Histograms 117 4.4.3 How Much Information Is There in a Few Bins? 120 Problems 122 5 Averaged Shifted Histograms 125 5.1 Construction 126 5.2 Asymptotic Properties 128 5.3 The Limiting ASH as a Kernel Estimator 133 Problems 135 6 Kernel Density Estimators 137 6.1 Motivation for Kernel Estimators 138 6.1.1 Numerical Analysis and Finite Differences 138 6.1.2 Smoothing by Convolution 139 6.1.3 Orthogonal Series Approximations 140 6.2 Theoretical Properties: Univariate Case 142 6.2.1 MISE Analysis 142 6.2.2 Estimation of Derivatives 144 6.2.3 Choice of Kernel 145 6.2.3.1 Higher Order Kernels 145 6.2.3.2 Optimal Kernels 151 6.2.3.3 Equivalent Kernels 153 6.2.3.4 Higher Order Kernels and Kernel Design 155 6.2.3.5 Boundary Kernels 157 6.3 Theoretical Properties: Multivariate Case 161 6.3.1 Product Kernels 162 6.3.2 General Multivariate Kernel MISE 164 6.3.3 Boundary Kernels for Irregular Regions 167 6.4 Generality of the Kernel Method 167 6.4.1 Delta Methods 167 6.4.2 General Kernel Theorem 168 6.4.2.1 Proof of General Kernel Result 168 6.4.2.2 Characterization of a Nonparametric Estimator 169 6.4.2.3 Equivalent Kernels of Parametric Estimators 171 6.5 Cross-Validation 172 6.5.1 Univariate Data 172 6.5.1.1 Early Efforts in Bandwidth Selection 173 6.5.1.2 Oversmoothing 176 6.5.1.3 Unbiased and Biased Cross-Validation 177 6.5.1.4 Bootstrapping Cross-Validation 181 6.5.1.5 Faster Rates and PI Cross-Validation 184 6.5.1.6 Constrained Oversmoothing 187 6.5.2 Multivariate Data 190 6.5.2.1 Multivariate Cross-Validation 190 6.5.2.2 Multivariate Oversmoothing Bandwidths 191 6.5.2.3 Asymptotics of Multivariate Cross-Validation 192 6.6 Adaptive Smoothing 193 6.6.1 Variable Kernel Introduction 193 6.6.2 Univariate Adaptive Smoothing 195 6.6.2.1 Bounds on Improvement 195 6.6.2.2 Nearest-Neighbor Estimators 197 6.6.2.3 Sample-Point Adaptive Estimators 198 6.6.2.4 Data Sharpening 200 6.6.3 Multivariate Adaptive Procedures 202 6.6.3.1 Pointwise Adapting 202 6.6.3.2 Global Adapting 203 6.6.4 Practical Adaptive Algorithms 204 6.6.4.1 Zero-Bias Bandwidths for Tail Estimation 204 6.6.4.2 UCV for Adaptive Estimators 208 6.7 Aspects of Computation 209 6.7.1 Finite Kernel Support and Rounding of Data 210 6.7.2 Convolution and Fourier Transforms 210 6.7.2.1 Application to Kernel Density Estimators 211 6.7.2.2 FFTs 212 6.7.2.3 Discussion 212 6.8 Summary 213 Problems 213 7 The Curse of Dimensionality and Dimension Reduction 217 7.1 Introduction 217 7.2 Curse of Dimensionality 220 7.2.1 Equivalent Sample Sizes 220 7.2.2 Multivariate L1 Kernel Error 222 7.2.3 Examples and Discussion 224 7.3 Dimension Reduction 229 7.3.1 Principal Components 229 7.3.2 Projection Pursuit 231 7.3.3 Informative Components Analysis 234 7.3.4 Model-Based Nonlinear Projection 239 Problems 240 8 Nonparametric Regression and Additive Models 241 8.1 Nonparametric Kernel Regression 242 8.1.1 The Nadaraya–Watson Estimator 242 8.1.2 Local Least-Squares Polynomial Estimators 243 8.1.2.1 Local Constant Fitting 243 8.1.2.2 Local Polynomial Fitting 244 8.1.3 Pointwise Mean Squared Error 244 8.1.4 Bandwidth Selection 247 8.1.5 Adaptive Smoothing 247 8.2 General Linear Nonparametric Estimation 248 8.2.1 Local Polynomial Regression 248 8.2.2 Spline Smoothing 250 8.2.3 Equivalent Kernels 252 8.3 Robustness 253 8.3.1 Resistant Estimators 254 8.3.2 Modal Regression 254 8.3.3 L1 Regression 257 8.4 Regression in Several Dimensions 259 8.4.1 Kernel Smoothing and WARPing 259 8.4.2 Additive Modeling 261 8.4.3 The Curse of Dimensionality 262 8.5 Summary 265 Problems 266 9 Other Applications 267 9.1 Classification, Discrimination, and Likelihood Ratios 267 9.2 Modes and Bump Hunting 273 9.2.1 Confidence Intervals 273 9.2.2 Oversmoothing for Derivatives 275 9.2.3 Critical Bandwidth Testing 275 9.2.4 Clustering via Mixture Models and Modes 277 9.2.4.1 Gaussian Mixture Modeling 277 9.2.4.2 Modes for Clustering 280 9.3 Specialized Topics 286 9.3.1 Bootstrapping 286 9.3.2 Confidence Intervals 287 9.3.3 Survival Analysis 289 9.3.4 High-Dimensional Holes 290 9.3.5 Image Enhancement 292 9.3.6 Nonparametric Inference 292 9.3.7 Final Vignettes 293 9.3.7.1 Principal Curves and Density Ridges 293 9.3.7.2 Time Series Data 294 9.3.7.3 Inverse Problems and Deconvolution 294 9.3.7.4 Densities on the Sphere 294 Problems 294 APPENDIX A Computer Graphics in R3 296 A.1 Bivariate and Trivariate Contouring Display 296 A.1.1 Bivariate Contouring 296 A.1.2 Trivariate Contouring 299 A.2 Drawing 3-D Objects on the Computer 300 APPENDIX B DataSets 302 B.1 US Economic Variables Dataset 302 B.2 University Dataset 304 B.3 Blood Fat Concentration Dataset 305 B.4 Penny Thickness Dataset 306 B.5 Gas Meter Accuracy Dataset 307 B.6 Old Faithful Dataset 309 B.7 Silica Dataset 309 B.8 LRL Dataset 310 B.9 Buffalo Snowfall Dataset 310 APPENDIX C Notation and Abbreviations 311 C.1 General Mathematical and Probability Notation 311 C.2 Density Abbreviations 312 C.3 Error Measure Abbreviations 313 C.4 Smoothing Parameter Abbreviations 313 REFERENCES 315 AUTHOR INDEX 334 SUBJECT INDEX 339

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Book SynopsisA comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies.Trade Review"This book maintains its uniqueness among the competition through its extensive referencing to proofs and comprehensive coverage of topics not found in any other one book." (International Statistical Review, December 2008) "This book maintains its uniqueness among the competition through its extensive referencing to proofs and comprehensive coverage of topics not found in any other one book." (International Statistical Review, Dec 2008) "This is an authoritative and comprehensive reference that will be useful to researchers who need to use the results of matrix analysis in their work. It would also be a useful addition to the reference collection of any mathematical library." (MAA Review, March 2008)Table of ContentsPreface. 1. Notation. 1.1 General Definitions. 1.2 Some Continuous Univariate Distributions. 1.3 Glossary of Notation. 2. Vectors, Vector Spaces, and Convexity. 2.1 Vector Spaces. 2.1.1 Definitions. 2.1.2 Quadratic Subspaces. 2.1.3 Sums and Intersections of Subspaces. 2.1.4 Span and Basis. 2.1.5 Isomorphism. 2.2 Inner Products. 2.2.1 Definition and Properties. 2.2.2 Functionals. 2.2.3 Orthogonality. 2.2.4 Column and Null Spaces. 2.3 Projections. 2.3.1 General Projections. 2.3.2 Orthogonal Projections. 2.4 Metric Spaces. 2.5 Convex Sets and Functions. 2.6 Coordinate Geometry. 2.6.1 Hyperplanes and Lines. 2.6.2 Quadratics. 2.6.3 Miscellaneous Results. 3. Rank. 3.1 Some General Properties. 3.2 Matrix Products. 3.3 Matrix Cancellation Rules. 3.4 Matrix Sums. 3.5 Matrix Differences. 3.6 Partitioned Matrices. 3.7 Maximal and Minimal Ranks. 3.8 Matrix Index. 4. Matrix Functions: Inverse, Transpose, Trace, Determinant, and Norm. 4.1 Inverse. 4.2 Transpose. 4.3 Trace. 4.4 Determinants. 4.4.1 Introduction. 4.4.2 Adjoint Matrix. 4.4.3 Compound Matrix. 4.4.4 Expansion of a Determinant. 4.5 Permanents. 4.6 Norms. 4.6.1 Vector Norms. 4.6.2 Matrix Norms. 4.6.3 Unitarily Invariant Norms. 4.6.4 M,N-Invariant Norms. 4.6.5 Computational Accuracy. 5. Complex, Hermitian, and Related Matrices. 5.1 Complex Matrices. 5.1.1 Some General Results. 5.1.2 Determinants. 5.2 Hermitian Matrices. 5.3 Skew-Hermitian Matrices. 5.4 Complex Symmetric Matrices. 5.5 Real Skew-Symmetric Matrices. 5.6 Normal Matrices. 5.7 Quaternions. 6. Eigenvalues, Eigenvectors, and Singular Values. 6.1 Introduction and Definitions. 6.1.1 Characteristic Polynomial. 6.1.2 Eigenvalues. 6.1.3 Singular Values. 6.1.4 Functions of a Matrix. 6.1.5 Eigenvectors. 6.1.6 Hermitian Matrices. 6.1.7 Computational Methods. 6.1.8 Generalized Eigenvalues. 6.1.9 Matrix Products 103. 6.2 Variational Characteristics for Hermitian Matrices. 6.3 Separation Theorems. 6.4 Inequalities for Matrix Sums. 6.5 Inequalities for Matrix Differences. 6.6 Inequalities for Matrix Products. 6.7 Antieigenvalues and Antieigenvectors. 7. Generalized Inverses. 7.1 Definitions. 7.2 Weak Inverses. 7.2.1 General Properties. 7.2.2 Products. 7.2.3 Sums and Differences. 7.2.4 Real Symmetric Matrices. 7.2.5 Decomposition Methods. 7.3 Other Inverses. 7.3.1 Reflexive (g12) Inverse. 7.3.2 Minimum Norm (g14) Inverse. 7.3.3 Minimum Norm Reflexive (g124) Inverse. 7.3.4 Least Squares (g13) Inverse. 7.3.5 Least Squares Reflexive (g123) Inverse. 7.4 Moore-Penrose (g1234) Inverse. 7.4.1 General Properties. 7.4.2 Sums. 7.4.3 Products. 7.5 Group Inverse. 7.6 Some General Properties of Inverses. 8. Some Special Matrices. 8.1 Orthogonal and Unitary Matrices. 8.2 Permutation Matrices. 8.3 Circulant, Toeplitz, and Related Matrices. 8.3.1 Regular Circulant. 8.3.2 Symmetric Regular Circulant. 8.3.3 Symmetric Circulant. 8.3.4 Toeplitz Matrix. 8.3.5 Persymmetric Matrix. 8.3.6 Cross-Symmetric (Centrosymmetric) Matrix. 8.3.7 Block Circulant. 8.3.8 Hankel Matrix. 8.4 Diagonally Dominant Matrices. 8.5 Hadamard Matrices. 8.6 Idempotent Matrices. 8.6.1 General Properties. 8.6.2 Sums of Idempotent Matrices and Extensions. 8.6.3 Products of Idempotent Matrices. 8.7 Tripotent Matrices. 8.8 Irreducible Matrices. 8.9 Triangular Matrices. 8.10 Hessenberg Matrices. 8.11 Tridiagonal Matrices. 8.12 Vandermonde and Fourier Matrices. 8.12.1 Vandermonde Matrix. 8.12.2 Fourier Matrix. 8.13 Zero-One (0,1) Matrices. 8.14 Some Miscellaneous Matrices and Arrays. 8.14.1 Krylov Matrix. 8.14.2 Nilpotent and Unipotent Matrices. 8.14.3 Payoff Matrix. 8.14.4 Stable and Positive Stable Matrices. 8.14.5 P-Matrix. 8.14.6 Z- and M-Matrices. 8.14.7 Three-Dimensional Arrays. 9. Non-Negative Vectors and Matrices. 9.1 Introduction. 9.1.1 Scaling. 9.1.2 Modulus of a Matrix. 9.2 Spectral Radius. 9.2.1 General Properties. 9.2.2 Dominant Eigenvalue. 9.3 Canonical Form of a Non-negative Matrix. 9.4 Irreducible Matrices. 9.4.1 Irreducible Non-negative Matrix. 9.4.2 Periodicity. 9.4.3 Non-negative and Non-positive Off-Diagonal Elements. 9.4.4 Perron Matrix. 9.4.5 Decomposable Matrix. 9.5 Leslie Matrix. 9.6 Stochastic Matrices. 9.6.1 Basic Properties. 9.6.2 Finite Homogeneous Markov Chain. 9.6.3 Countably Infinite Stochastic Matrix. 9.6.4 Infinite Irreducible Stochastic Matrix. 9.7 Doubly Stochastic Matrices. 10. Positive Definite and Non-negative Definite Matrices. 10.1 Introduction. 10.2 Non-negative Definite Matrices. 10.2.1 Some General Properties. 10.2.2 Gram Matrix. 10.2.3 Doubly Non-negative Matrix. 10.3 Positive Definite Matrices. 10.4 Pairs of Matrices. 10.4.1 Non-Negative or Positive Definite Difference. 10.4.2 One or More Non-Negative Definite Matrices. 11. Special Products and Operators. 11.1 Kronecker Product. 11.1.1 Two Matrices. 11.1.2 More Than Two Matrices. 11.2 Vec Operator. 11.3 Vec-Permutation (Commutation) Matrix. 11.4 Generalized Vec-Permutation Matrix. 11.5 Vech Operator. 11.5.1 Symmetric Matrix. 11.5.2 Lower Triangular Matrix. 11.6 Star Operator. 11.7 Hadamard Product. 11.8 Rao-Khatri Product. 12. Inequalities. 12.1 Cauchy-Schwarz inequalities. 12.1.1 Real Vector Inequalities and Extensions. 12.1.2 Complex Vector Inequalities. 12.1.3 Real Matrix Inequalities. 12.1.4 Complex Matrix Inequalities. 12.2 H?older?s Inequality and Extensions. 12.3 Minkowski?s Inequality and Extensions. 12.4 Weighted Means. 12.5 Quasilinearization (Representation Theorems). 12.6 Some Geometrical Properties. 12.7 Miscellaneous Inequalities. 12.7.1 Determinants. 12.7.2 Trace. 12.7.3 Quadratics. 12.7.4 Sums and Products. 12.8 Some Identities. 13. Linear Equations. 13.1 Unknown vector. 13.1.1 Consistency. 13.1.2 Solutions. 13.1.3 Homogeneous Equations. 13.1.4 Restricted Equations. 13.2 Unknown Matrix. 13.2.1 Consistency. 13.2.2 Some Special Cases. 14. Partitioned Matrices. 14.1 Schur Complement. 14.2 Inverses. 14.3 Determinants. 14.4 Positive and Non-Negative Definite matrices. 14.5 Eigenvalues. 14.6 Generalized Inverses. 14.6.1 Weak Inverses. 14.6.2 Moore-Penrose Inverses. 14.7 Miscellaneous partitions. 15. Patterned Matrices. 15.1 Inverses. 15.2 Determinants. 15.3 Perturbations. 15.4 Matrices With Repeated Elements and Blocks. 15.5 Generalized Inverses. 15.5.1 Weak Inverses. 15.5.2 Moore-Penrose Inverses. 16. Factorization of Matrices. 16.1 Similarity Reductions. 16.2 Reduction by Elementary Transformations. 16.2.1 Types of Transformation. 16.2.2 Equivalence Relation. 16.2.3 Echelon Form. 16.2.4 Hermite Form. 16.3 Singular Value Decomposition (SVD). 16.4 Triangular Factorizations. 16.5 Orthogonal-Triangular Reductions. 16.6 Further Diagonal or Tridiagonal Reductions. 16.7 Congruence. 16.8 Simultaneous Reductions. 16.9 Polar Decomposition. 16.10 Miscellaneous Factorizations. 17. Differentiation and Finite Differences. 17.1 Introduction. 17.2 Scalar Differentiation. 17.2.1 Differentiation with Respect to t. 17.2.2 Differentiation With Respect to a Vector Element. 17.2.3 Differentiation With Respect to a Matrix Element. 17.3 Vector Differentiation: Scalar Function. 17.3.1 Basic Results. 17.3.2 x=vec X. 17.3.3 Function of a Function. 17.4 Vector Differentiation: Vector Function. 17.5 Matrix Differentiation: Scalar Function. 17.5.1 General Results. 17.5.2 f = trace. 17.5.3 f = determinant. 17.5.4 f = yrs. 17.5.5 f = eigenvalue. 17.6 Transformation Rules. 17.7 Matrix Differentiation: Matrix Function. 17.8 Matrix Differentials. 17.9 Perturbation Using Differentials. 17.10 Matrix Linear Differential Equations. 17.11 Second Order Derivatives. 17.12 Vector Difference Equations. 18. Jacobians. 18.1 Introduction. 18.2 Method of Differentials. 18.3 Further Techniques. 18.3.1 Chain Rule. 18.3.2 Exterior (Wedge) Product of Differentials. 18.3.3 Induced Functional Equations. 18.3.4 Jacobians Involving Transposes. 18.3.5 Patterned Matrices and L-Structures. 18.4 Vector Transformations. 18.5 Jacobians for Complex Vectors and Matrices. 18.6 Matrices with Functionally Independent Elements. 18.7 Symmetric and Hermitian Matrices. 18.8 Skew-Symmetric and Skew-Hermitian Matrices. 18.9 Triangular Matrices. 18.9.1 Linear Transformations. 18.9.2 Nonlinear Transformations of X. 18.9.3 Decompositions With One matrix Skew Symmetric. 18.9.4 Symmetric Y. 18.9.5 Positive Definite Y. 18.9.6 Hermitian Positive Definite Y. 18.9.7 Skew Symmetric Y. 18.9.8 LU Decomposition. 18.10 Decompositions Involving Diagonal Matrices. 18.10.1 Square Matrices. 18.10.2 One Triangular Matrix. 18.10.3 Symmetric and Skew Symmetric Matrices. 18.11 Positive?Definite Matrices. 18.12 Caley Transformation. 18.13 Diagonalizable Matrices. 18.14 Pairs of Matrices. 19. Matrix Limits, Sequences and Series. 19.1 Limits. 19.2 Sequences. 19.3 Asymptotically Equivalent Sequences. 19.4 Series. 19.5 Matrix Functions. 19.6 Matrix Exponentials. 20. Random Vectors. 20.1 Notation. 20.2 Variances and Covariances. 20.3 Correlations. 20.3.1 Population Correlations. 20.3.2 Sample Correlations. 20.4 Quadratics. 20.5 Multivariate Normal Distribution. 20.5.1 Definition and Properties. 20.5.2 Quadratics in Normal Variables. 20.5.3 Quadratics and Chi-squared. 20.5.4 Independence and Quadratics. 20.5.5 Independence of Several Quadratics. 20.6 Complex Random Vectors. 20.7 Regression Models. 20.7.1 V is the Identity Matrix. 20.7.2 V is Positive Definite. 20.7.3 V is Non-negative Definite. 20.8 Other Multivariate Distributions. 20.8.1 Multivariate t-Distribution. 20.8.2 Elliptical and Spherical Distributions. 20.8.3 Dirichlet Distributions. 21. Random Matrices. 21.1 Introduction. 21.2 Generalized Quadratic Forms. 21.2.1 General Results. 21.2.2 Wishart Distribution. 21.3 Random Samples. 21.3.1 One Sample. 21.3.2 Two Samples. 21.4 Multivariate Linear Model. 21.4.1 Least Squares Estimation. 21.4.2 Statistical Inference. 21.4.3 Two Extensions. 21.5 Dimension Reduction Techniques. 21.5.1 Principal Component Analysis (PCA). 21.5.2 Discriminant Coordinates. 21.5.3 Canonical Correlations and Variates. 21.5.4 Latent Variable Methods. 21.5.5 Classical (Metric) Scaling. 21.6 Procrustes Analysis (Matching Configurations). 21.7 Some Specific Random Matrices. 21.8 Allocation Problems. 21.9 Matrix Variate Distributions. 21.10 Matrix Ensembles. 22. Inequalities for Probabilities and Random Variables. 22.1 General Probabilities. 22.2 Bonferroni-Type Inequalities. 22.3 Distribution-Free Probability Inequalities. 22.3.1 Chebyshev-Type Inequalities. 22.3.2 Kolmogorov-Type Inequalities. 22.3.3 Quadratics and Inequalities. 22.4 Data Inequalities. 22.5 Inequalities for Expectations. 22.6 Multivariate Inequalities. 22.6.1 Convex Subsets. 22.6.2 Multivariate Normal. 22.6.3 Inequalities For Other Distributions. 23. Majorization. 23.1 General Properties. 23.2 Schur Convexity. 23.3 Probabilities and Random variables. 24. Optimization and Matrix Approximation. 24.1 Stationary Values. 24.2 Using Convex and Concave Functions. 24.3 Two General Methods. 24.3.1 Maximum Likelihood. 24.3.2 Least Squares. 24.4 Optimizing a Function of a Matrix. 24.4.1 Trace. 24.4.2 Norm. 24.4.3 Quadratics. 24.5 Optimal Designs. References. Index.

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Book SynopsisA textbook for advanced undergraduate/first year graduate level courses in statistical methods in geography. Presents methods useful in research design, hypothesis testing, and analyzing spatial and functional relationships.Table of ContentsAn Introduction to Statistical Methods. The Display of Distributions. Statistical Summaries of Distributions. Probability and Probability Functions. Sampling Designs and Sampling Methods. Statistical Inference: Fitting Probability Functions. Statistical Inference: Interval Estimation and HypothesisTesting. An Introduction to Bivariate Relationships. The Simple Linear Regression Model. The General Linear Model--Multiple Regression. Issues in the Application of the General Linear Model. Extensions of Multivariate Linear Regression Methods. Alternative Forms of Multivariate Analysis. Index.

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Book SynopsisGlobal and combinatorial optimization heuristics are widely used in different areas ranging from engineering to operational research. This introduction to the fast growing field of optimization heuristics offers the knowledge to use the techniques in a number of different application areas.Trade Review"For statisticians and econometricians with a general interest in new optimization paradigms, Winker...introduces optimization heuristics for application..." (Reference Research Book News, Vol. 16, No. 3, August 2001) "...a very fine textbook ... does an excellent job of motivating ones . interests in optimization heuristics." (Technometrics, Vol. 43, No. 4, November 2001) "a text that comprehensively addresses this 'art' is to be congratulated..." (Short Book Reviews, August 2002) ..."The book is recommend ... the postgraduate students the book provides a valuable introduction to optimization heuristics." (Zentralblatt MATH, Vol.1001, No.01, 2003)Table of ContentsPreface. Introduction. OPTIMIZATION IN STATISTICS AND ECONOMETRICS. Optimization in Economics. Optimization in Statistics and Econometrics. The Heuristic Optimization Paradigm. HEURISTIC OPTIMIZATION: THRESHOLD ACCEPTING. Optimization Methods. The Global Optimization Heuristic Threshold Accepting. Relative Performance of Threshold Accepting. Tuning of Threshold Accepting. A Practical Guide to the Implementation of Threshold Accepting. APPLICATIONS IN STATISTICS AND ECONOMETRICS. Introduction. Experimental Design. Identification of Multivariate Lag Structures. Optimal Aggregation. Censored Quantile Regression. Continuous Global Optimization. CONCLUSION AND OUTLOOK. Conclusion. Outlook for Further Research. References. List of Symbols. Author Index. Subject Index.

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Book SynopsisThe only way to recommend new crop varieties, agrochemicals and husbandry systems is after they have been thoroughly tested in a series of replicated field trials. The trials, which are used to test these products or systems, need to be designed in such a way that the results obtained are reasonable and representative.Trade Review"...suitable for a practical course to science students wishing to appreciate statistical methods in agricultural and environmental research." (Short Book Reviews, Vol. 21, No. 2, August 2001) "...useful to undergraduate students..." (Zentralblatt MATH, Vol. 961, 2001/11)Table of ContentsPreface. Basic Principles of Experimentation. Basic Statistical Calculations. Basic Data Summary. The Normal Distribution, the t-Distribution and Confidence Intervals. Introduction to Hypothesis Testing. Comparison of Two Independent Sample Means. Linear Regression and Correlation. Curve Fitting. The Completely Randomised Design. The Randomised Block Design. The Latin Square Design. Factorial Experiments. Comparison of Treatment Means. Checking the Assumptions and Transformation of Data. Missing Values and Incomplete Blocks. Split Plot Designs Comparison of Regression Lines and Analysis of Covariance. Analysis of Counts. Some Non-parametric Methods. Appendix 1: The Normal Distribution Function. Appendix 2: Percentage Points of the Normal Distribution. Appendix 3: Percentage Points of the t-Distribution. Appendix 4a: 5 Per Cent Points of the F-Distribution. Appendix 4b: 2.5 Per Cent Points of the F-Distribution. Appendix 4c: 1 Per Cent Points of the F-Distribution. Appendix 4d: 0.1 Per Cent Points of the F-Distribution. Appendix 5: Percentage Points of the Sample Correlation Coefficient (r) When the Population Correlation Coefficient is 0 and n is the Number of X.Y. Pairs. Appendix 6: 5 Per Cent Points of the Studentised Range, for Use in Tukey and SNK Tests. Appendix 7: Percentage Points of the Chi-Square Distribution. Appendix 8: Probabilities of S or Fewer Successes in the Binomial Distribution with n 'trials' and p = 0.5. Appendix 9: Critical Values of T in the Wilcoxon Signed Rank or Matched Pairs Test. Appendix 10: Critical Values of U in the Mann-Whitney Test. References. Further Reading. Index.

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Book SynopsisThis volume provides a thorough account of key basic concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. It presents a novel discussion of model comparison and choice from a Bayesian perspective.Table of ContentsFoundations. Generalisations. Modelling. Inference. Remodelling. Appendices. References. Indexes.

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Book SynopsisThis textbook aims to clarify the links between statistics and computerized data analysis when applying the scientific method of enquiry to geography. It explains basic statistical techniques and demonstrates their application in geographical data analysis.Table of ContentsPartial table of contents: The Nature of Geographical Data. Inputting Geographical Data on to the Computer. STATISTICAL ANALYSIS I. Descriptive Statistics. STATISTICAL ANALYSIS II. An Introduction to Hypothesis Testing. An Overview of Probability Distributions. STATISTICAL ANALYSIS III. Spatial Statistics. Appendices. References and Selected Bibliography. Index.

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Book SynopsisChange-point problems arise in a variety of experimental andmathematical sciences, as well as in engineering and healthsciences. This rigorously researched text provides a comprehensivereview of recent probabilistic methods for detecting various typesof possible changes in the distribution of chronologically orderedobservations. Further developing the already well-establishedtheory of weighted approximations and weak convergence, the authorsprovide a thorough survey of parametric and non-parametric methods,regression and time series models together with sequential methods.All but the most basic models are carefully developed with detailedproofs, and illustrated by using a number of data sets. Contains athorough survey of: * The Likelihood Approach * Non-Parametric Methods * Linear Models * Dependent Observations This book is undoubtedly of interest to all probabilists andstatisticians, experimental and health scientists, engineers, andessential for those wTrade Review"This book is suitable for Ph.D. students who wish to establish a solid grounding in the field, and researchers who need a reliable reference to precisely formulated results and their proofs. The book contains a very extensive list of references reading into the late 1990's." (Mathematical Reviews, 2011)Table of ContentsThe Likelihood Approach. Nonparametric Methods. Linear Models. Dependent Observations. Appendix. References. Indexes.

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Book SynopsisThis monograph covers basic theoretical results and differing methods for calculating probability and quantile functions. It compares numerical algorithms for the solution of stochastic programming problems with probabilistic objectives.Table of ContentsStochastic Programming Models with Probability and QuantileObjective Functions. Basic Properties of Probabilistic Problems. Estimates and Bounds for Probabilities and Quantiles. Methods and Algorithms for Solving Probabilistic Problems. Notation List. Index.

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Book SynopsisClearly written and free of statistical jargon, this invaluable guide concentrates on the practicalities of statistical analysis for anyone involved with agricultural research. Each section starts with the key points, giving a quick reference to the contents and plenty of examples using a reala data.Table of ContentsAcknowledgements INTRODUCTION Notation A little history Population versus samples PLANNING Formulating the idea Defining objectives Defining the population Formulating hypotheses Hypothesis testing Anticipating treatment differences DESIGN Variables Choosing the treatments Constraints Replication Blocking Randomization Covariants Confounding TRIAL STRUCTURE Considerations Single-treatment factor designs Multi-treatment factor designs Some other designs DATA ENTRY AND EXPLORATION Data entry Data Data checking Data exploration ANALYTICAL TECHNIQUES Parametric techniques Non-parametric techniques Comparison of parametric and non-parametric techniques OTHER STATISTICAL TECHNIQUES Multivariate analysis Time series analysis ASPECTS OF COMPUTING APPENDICES Glossary of Statistical Terms Analysis of Variance Formulae INDEX

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Book SynopsisThe concepts of epidemiology, the science that uses statistical methods to investigate associations between risk factors and disease outcomes in human populations, are developed using examples involving real data from published studies.Table of ContentsEpidemiological Research. Statistical Methods I. Statistical Methods II. Mantel-Haenzel Methods. Logistic Regression. Logistic Regression II. Survival Analysis. Matching. Sample Size. Appendix. Index.

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Book SynopsisStatistics in Practice A new series of practical books outliningthe use of statistical techniques in a wide range of applicationareas: Human and Biological Sciences Earth and Environmental Sciences Industry, Commerce and Finance The authors of this important text explore the processes throughwhich archaeologists analyse their data and how these can be mademore rigorous and effective by sound statistical modelling. Theyassume relatively little previous statistical or mathematicalknowledge. Introducing the idea underlying the Bayesian approach tothe statistical analysis of data and their subsequentinterpretation, the authors demonstrate the major advantage of thisapproach, i.e. that it allows the incorporation of relevant priorknowledge or beliefs into the analysis. By doing so it provides alogical and coherent way of updating beliefs from those held beforeobserving the data to those held after taking the data intoaccount. To illustrTable of ContentsThe Bayesian Approach to Statistical Archaeology. Outline of the Approach. Modelling in Archaeology. Quantifying Uncertainty: The Probability Concept. Statistical Modelling. Bivariate and Multivariate Distributions. Bayesian Inference. Implementation Issues. Interpretation of Radiocarbon Results. Spatial Analysis. Sourcing and Provenancing. Application to Other Dating Methods. The Way Forward. References. Index.

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Book SynopsisProviding a unified coverage of the latest research and applications methods and techniques, this book is devoted to two interrelated techniques for solving some important problems in machine intelligence and pattern recognition, namely probabilistic reasoning and computational learning. The contributions in this volume describe and explore the current developments in computer science and theoretical statistics which provide computational probabilistic models for manipulating knowledge found in industrial and business data. These methods are very efficient for handling complex problems in medicine, commerce and finance. Part I covers Generalisation Principles and Learning and describes several new inductive principles and techniques used in computational learning. Part II describes Causation and Model Selection including the graphical probabilistic models that exploit the independence relationships presented in the graphs, and applications of Bayesian networks to multivariate statisticTable of ContentsPartial table of contents: GENERALISATION PRINCIPLES AND LEARNING. Structure of Statistical Learning Theory (V. Vapnik). MML Inference of Predictive Trees, Graphs and Nets (C.Wallace). Probabilistic Association and Denotation in Machine Learning ofNatural Language (P. Suppes & L. Liang). CAUSATION AND MODEL SELECTION. Causation, Action, and Counterfactuals (J. Pearl). Efficient Estimation and Model Selection in Large Graphical Models(D. Wedelin). BAYESIAN BELIEF NETWORKS AND HYBRID SYSTEMS. Bayesian Belief Networks and Patient Treatment (L. Meshalkin &E. Tsybulkin). DECISION-MAKING, OPTIMIZATION AND CLASSIFICATION. Axioms for Dynamic Programming (P. Shenoy). Extreme Values of Functionals Characterizing Stability ofStatistical Decisions (A. Nagaev). Index.

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Book SynopsisPioneered by David Kendall, the statistical theory of shape is an emerging area generating considerable interest for statisticians, engineers, and computer scientists. Co--written by Dr. Kendall, this volume presents a coherent theory of shape developed from Kendalla s own approach known as static and kinematic theory.Trade Review"This is a fascinating book mixing geometry, topology and probability theory..." (London Mathematical Society Bulletin, Vol 32, 2000) "The potential value that his volume should have to researchers in many areas for years to come." (Short Book Reviews, August 2000) "I would like to conclude this review by strongly recommending that geodists have this book on desk within ready reach of hands" (Journal of Geodesy, Vol. 75, 2001) "...a mathematical jewel..." (Mathematical Reviews, 2003g)Table of ContentsShapes and Shape Spaces. The Global Structure of Shape Spaces. Computing the Homology of Cell Complexes. A Chain Complex for Shape Spaces. The Homology Groups of Shape Spaces. Geodesics in Shape Spaces. The Riemannian Structure of Shape Spaces. Induced Shape-Measures. Mean Shapes and the Shape of the Means. Visualising the Higher Dimensional Shape Spaces. General Shape Spaces. Appendix. Bibliography. Index.

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Book SynopsisOffers an introduction in Applied Statistics focusing on some of the statistics of today''s society--world wide population growth, economic developments, international trade and energy consumption, global maldistribution of income and absorption of resources, depletion of species and resources, environmental changes, and human problems.Table of ContentsThe Global Situation. Primary and Secondary Magnitudes. Ratios. Percentages. The Arithmetic Mean. Time Series. The Distribution of World Product. Indices. The Population Explosion. Regression and Correlation. Frequency Distributions. Bringing It All Together. Bibliography. Index.

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Book SynopsisMatrices are used in many fields such as statistics, econometrics, mathematics, natural sciences and engineering. They provide a concise, simple method for describing long and complicated computations. This is a comprehensive handbook and dictionary of terms for matrix theory.Table of ContentsDefinitions, Notations, Terminology. Rules for Matrix Operations. Matrix Valued Functions of a Matrix. Trace, Determinant and Rank of a Matrix. Eigenvalues and Singular Values. Matrix Decompositions and Canonical Forms. Vectorization Operators. Vector and Matrix Norms. Properties of Special Matrices. Vector and Matrix Derivatives. Polynomials, Power Series and Matrices. Appendix. References. Index.

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Book SynopsisHájek was undoubtedly a statistician of enormous power who, in his relatively short life, contributed fundamental results over a wide range of topics... V. Barnett, University of Nottingham. Hájek''s writings in statistics are not only seminal but form a powerful unified body of theory. This is particularly the case with his studies of non-parametric statistics. His book The Theory of Rank Test, with ?idák, was described by W. Hoeffding as almost the last word on the subject. Hájek''s work still has great importance today, for example his research has proved highly relevant to recent investigations on bootstrap diagnostics. Much of Hájek''s work is scattered through the literature and some of it quite inaccessible, existing only in the original Czech version. This book provides a valuable unified text of the collective works of Hájek with additional essays by internationally renowned contributors. Undoubtedly this book will be essential reading to modern researchers in nonparametriTable of ContentsHISTORICAL OVERVIEW. Biography of Jaroslav Hájek. Hájek and the Superefficiency Breakthrough. Jaroslav Hájek and His Impact on the Theory of Rank Tests. Recollection of My Contacts with Jaroslav Hájek. On Some Early Papers of Jaroslav Hájek. Contributions of Jaroslav Hájek to Statistical Inference on Stochastic Processes. The Hájek Perspectives in Finite Population Sampling. Publications of Jaroslav Hájek. Hájek PhD Students. COLLECTED WORKS OF JAROSLAV HÁJEK Representative Cluster Sampling by a Method of Two Phases. Some Rank Distributions and Their Applications. Generalization of an Inequality of Kolmogorov. Asymptotic Efficiency of a Certain Sequence of Tests. Linear Estimation of the Mean Value of a Stationary Random Process with Convex Correlation Function. Inequalities for the Generalized Student's Distribution and their Applications. Predicting a Stationary Process when the Correlation Function is Convex. A Property of J-Divergence of Marginal Probability Distributions. On a Property of Normal Distributions of Any Stochastic Process. On the Distribution of Some Statistics in the Presence of Intraclass Correlation. On the Theory of Ratio Estimates. Some Contributions to the Theory of Probability Sampling. Optimum Strategy and Other Problems in Probability Sampling. On a Simple Linear Model in Gaussian Processes. Limiting Distributions in Simple Random Sampling from a Finite Population. On Plane Sample and Related Geometrical Problems. Some Extensions of the Wald-Wolfowitz-Noether Theorem. On Linear Estimation Theory for an Infinite Number of Observations. Concerning Relative Accuracy of Stratified and Systematic Sampling in a Plane. On Linear Statistical Problems in Stochastic Processes. An Inequality Concerning Random Linear Functionals on a Linear Space with a Random Norm and Its Statistical Application. Asymptotically Most Powerful Rank-Order Tests. Cost Minimization in Miltiparameter Estimation. Asymptotic Theory of Rejective Sampling with Varying Probabilities from a Finite Population. Extension of the Kolmogorov-Smirnov Test to Regression Alternatives. On Basic Concepts of Statistics. Locally Most Powerful Rank Tests of Independence. Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives. Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II. Miscellaneous Problems of Rank Test Theory. A Characterization of Limiting Distributions of Regular Estimates. Limiting Properties of Likelihoods and Inference. Local Asymptotic Minimax and Admissibility in Estimation. Asymptotic Sufficiency of the Vector of Ranks in the Bahadur Sense. Regression Designs in Autoregressive Stochastic Processes. Asymptotic Theories of Sampling with Varying Probabilities without Replacement.

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Book SynopsisStatistical inference is the process of drawing conclusions based upon the available data on the measurement of uncertainty of a defined event. It allows one to draw a conclusion or a generalization from the available data. , i.e. if there is smoke there is a good probability there is a fire.Table of ContentsIntroduction: Statistical Inference and Decision-making. An Illustration of the Different Approaches. Probability. Utility and Decision-making. Classical Inference. Bayesian Inference. Decision Theory. Other Approaches. Perspective. References. Index.

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Book SynopsisDecision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author''s fluent style will leave the reader with an avid interest in the subject. * Tailored to the needs of students of optimization and decision theory * Written in a lucid style with numerous examples and applications * Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity * Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics * Coverage of advanced topics: Markov decision procesTable of ContentsIntroduction; PART I: Deterministic Models; Multi-Stage Decision Problems; Networks; Further Applications; Convexity; PART II: Stochastic Models; General Principles; Optimal Stopping; Special Problems; PART III: Markov Decision Processes; General Theory; Minimising Average Costs; Statistical Decision

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Book SynopsisReflecting the current high level of interest in the application of the principle of mathematical induction to the solution of optimization problems, this book offers a comprehensive introduction to the field.Trade Review"This textbook...draws on his many years of experience in teaching this topic as well as on his considerable professional expertise in the area. It is ideally suited to its stated purpose as a student text." (Short Book Reviews, Vol. 20. No. 3, December 2000) "...I was impressed with this book..." (The Statistician, Vol.51, No.2 2002) "...excellent for the audience to whom it is addressed, and it is to be hoped that the author will write a further textbook..." (Jnl of the Operational Research Society, Vol 54(10) 2003)Table of ContentsPreface xi 1 Introduction 1 1.1 Mathematical Induction 1 1.2 Historical Background 2 1.3 Dynamic Programming 5 1.4 The Executioner’s Tale 8 1.5 Summary 8 Exercises 10 I Deterministic Models 11 2 Multi-Stage Decision Problems 13 2.1 Maximizing Utilities 13 2.2 A General Model 17 2.3 Applications 19 Exercises 25 3 Networks 27 3.1 Shortest Paths 27 3.2 Directed Networks 29 3.3 Critical Path Analysis 30 Exercises 37 4 Further Applications 39 4.1 Discrete Actions 39 4.2 The Knapsack Problem 39 4.3 A Simple Replacement Model 42 4.4 Scheduling Problems 44 4.5 Johnson’s Algorithm 45 Exercises 49 5 Convexity 51 5.1 Convex and Concave Functions 51 5.2 Allocation Problems 56 5.3 Concave Utility Functions 60 Exercises 64 II Stochastic Models 67 6 Markov Systems 69 6.1 Introduction 69 6.2 Stochastic Dynamic Programming 70 6.3 Applications 72 Exercises 78 7 Optimal Stopping 79 7.1 Introduction 79 7.2 Stopping Times and Stopping Sets 82 7.3 Applications 90 Exercises 94 8 Special Problems 97 8.1 Introduction 97 8.2 Selling an Asset 97 8.3 The Marriage Problem 104 8.4 Prophet Inequalities 109 Exercises 116 III Markov Decision Processes 119 9 General Theory 121 9.1 Introduction 121 9.2 Minimizing Discounted Expectations 122 9.3 Policy Improvements 130 9.4 A Machine Replacement Model 137 10 Minimizing Average Costs 145 10.1 Introduction 145 10.2 Long-Term Average Costs 148 10.3 Extension to Infinitely Many States 153 10.4 Optimal Inventory Policies 158 11 Statistical Decisions 165 11.1 Introduction 165 11.2 Testing Statistical Hypotheses 166 11.3 The Sequential Probability Ratio Test 170 Notes On the Exercises 177 Chapter 1 177 Chapter 2 177 Chapter 3 178 Chapter 4 179 Chapter 5 179 Chapter 6 180 Chapter 7 181 Chapter 8 183 References 185 Index 187

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Book SynopsisProvides an excellent introductory text for students on the principles and methods of statistical analysis in the life sciences, helping them choose and analyse statistical tests for their own problems and present their findings.Table of ContentsMeasurement and Sampling Concepts. Processing Data. Presenting Data. Measuring the Average. Measuring Variability. Probability. Probability Distributions as Models of Dispersion. The Normal Distribution. Data Transformation. How Good are Our Estimates? The Basis of Statistical Testing. Analysing Frequencies. Measuring Correlations. Regression Analysis. Comparing Averages. Analysis of Variance - ANOVA. Multivariate Analysis. Appendices. Bibliography and Further Reading. Index.

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Book SynopsisSpatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization.Trade Review"While this edition maintains the overall structure of the first, there are substantial changes in the content..." (Mathematical Reviews, Issue 2001c) "...a must..." (Monatshefte fur Mathematik, Vol 131/2, 2000)Table of ContentsDefinitions and Basic Properties of Voronoi Diagrams. Generalizations of the Voronoi Diagram. Algorithms for Computing Voronoi Diagrams. Poisson Voronoi Diagrams. Spatial Interpolation. Models of Spatial Processes. Point Pattern Analysis. Locational Optimization Through Voronoi Diagrams. References. Index.

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Book SynopsisMultilevel modelling facilitates the analysis of hierarchical data where observations may be nested within higher levels of classification. In health care research, for example, a study may be undertaken to determine the variability of patient outcomes where these also vary by hospital or health care region.Trade Review"...contains 13 well written chapters by experts...the references are recent and useful. It can be used as a textbook in graduate level modeling course." (Journal of Statistical Computation & Simulation, May 2004) "...exhibits a marvellous degree of coherence and clarity..." (Pharmaceutical Statistics, Vol 2, 2003) "...good introductions to multilevel models, and plenty of examples..." (Zentralblatt Math, 2003) "...I believe that the book all in all fulfils this promise..." (Statistics in Medicine, No.21, 2002) "...a very readable book whose audience does not seem to be limited to statisticians." (Technometrics, Vol. 44, No. 4, November 2002) "Highly recommended to biostatisticians, health care professionals and public health researchers in the application of multilevel model. It can also be used as a reference book for postgraduate students studying medical statistics." (ISCB News, December 2001)Table of ContentsPreface. Contributors. Introduction. Multilevel Data and Their Analysis (M. Healy). Modelling Repeated Measurements (H. Glodstein and G. Woodhouse). Binomial Regression (N. Rice). Poisson Regression (I. Langford and R. Day). Multivariate Multilevel Models (A. McLeod). Outliers, Robustness and the Detection of Discrepant Data (T. Lewis and I. Langford). Modelling Non-Hierarchical Structures (J. Rasbash and W. Browne). Multinomial Regression (M. Yang). Institutional Performance (E. Marshall and D. Spiegelhalter). Spatial Analysis (A. Leyland). Sampling (T. Snijders). Further Topics in Multilevel Modelling (H. Goldstein and A. Leyland). Software for Multilevel Analysis (J. de Leeuw and I. Kreft). References. Index.

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Book SynopsisThis work is a guide to the principles behind sensitivity analysis. It suggests suitable methods for particular types of problem, which allows a greater understanding of the entire causal assessment chain. This makes the impact of source uncertainties and framing assumptions more transparent.Trade Review"The book has a fair price...I think this is a book that everyone who does modeling should buy. It can readily be read piecemeal...so it is ideal for leisurely self-study..." (Technometrics Vol. 42, No. 4 May 2001) "...this book will prove helpful in the solution of many modeling problems." (La Doc Sti, September 2000) "...presents many different sensitivity analysis methodologies and demonstrates their usefulness in scientific research." (Zentralblatt MATH, Vol. 961, 2001/11)Table of ContentsWhat is Sensitivity Analysis. Hitchhiker's Guide to Sensitivity Analysis. METHODS. Designs of Experiments. Screening Methods. Local Methods. Sampling-Based Methods. Reliability Algorithms: FORM and SORM Methods. Variance-Based Methods. Managing the Tyranny of Parameters in Mathematical Modelling of Physical Systems. Bayesian Sensitivity Analysis. Graphical Methods. APPLICATIONS. Practical Experience in Applying Sensitivity and Uncertainty Analysis. Scenario and Parametric Sensitivity and Uncertainty Analysis in Nuclear Waste Disposal Risk Assessment: The Case of GESAMAC. Sensitivity Analysis for Signal Extraction in Economic Time Series. A Dataless Precalibration Analysis in Solid State Physics. Appplication of First-Order (FORM) and Second-Order (SORM) Reliability Methods: Analysis and Interpretation of Sensitivity Measures Related to Groundwater Pressure Decreases and Resulting Ground Subsidence. One-at-a-Time and Mini-Global Analyses for Characterizing Model Sensitivity in the Nonlinear Ozone Predictions from the US EPA Regional Acid Deposition Model (RADM). Comparing Different Sensitivity Analysis Methods on a Chemical Reactions Model. An Application of Sensitivity Analysis to Fish Population Dynamics. Global Sensitivity Analysis: A Quality Assurance Tool in Environmental Policy Modelling. CONCLUSIONS. Assuring the Quality of Models Designed for Predictive Tasks. Fortune and Future of Sensitivity Analysis. References. Appendix. Index.

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Book SynopsisStatistics in Geography has established itself as the best introductory textbook on the subject: the author makes statistical concepts and techniques intellible and their applications in a wide variety of problems comprehensible, even exciting. The main feature of this much-awaited new edition is a set of 17 computer programs (with sample outputs) that cover nearly all the statistical techniques described. These have been carefully written to be user-friendly in an elementary subset of Basic to make them simple to implement on most micro computers. This means students can be more adventurous in their applications and interpretations of statistical techniques. The author has, at the same time, retained all the worked examples in the book so that the reader can gain insight into the logic of the methds by working through them by hand. These, together with problems of various levels of complexity plus comprehensive answers at the back of the book, provide the student with a clear aTrade Review Reviews of the first edition ‘… the book is one of the most successful among statistical geography texts in achieving its aim of a clear, painless, and well-illustrated introduction to difficult concepts.’ Geographical Analysis ‘Highly recommended for its clarity and exemplification … the author and publishers have certainly made the text clear, easily readable an interesting with many good figures and tables, worked examples and directly related exercises with 18 pages of answers and explanations to the latter.’ Royal Statistical Society ‘The features I particularly like are the number of examples and class exercises, the constant attempts to relate each method back to statistical theory, and the useful diagrams. The author succeeds at showing why statistical tests have sampling distributions, produces some outstanding diagrams to illustrate linear regression, and has a fine set of statistical tables.’ Journal of GeographyTable of ContentsPreface of the Second Edition. Preface of the First Edition. Statistical Concepts. Description. Samples and Sampling. Comparisons. Relationships. Trends. Spatial Statistics. References. Appendix A: Answers to Exercises. Appendix B: Probability Tables. Appendix C: Tables of Critical Values. Appendix D: Random Numbers. Appendix E: Data Matrix. Appendix F: Notes for Programmers. Index.

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Book SynopsisUsing game theory and examples of actual games people play, this work shows how the elements of chance and rules underlie all that happens in the universe, from genetic behavior through economic growth to the composition of music. It also presents games derived from scientific models for equilibrium, selection, growth, and the composition of RNA.Trade Review"Fascinating ... has the character of the deepest sort of discussion among brilliant friends."--The New Yorker "Remarkable, fascinating, and very profound."--The New York Times Book ReviewTable of ContentsTranslators' NoteAcknowledgmentsForewordForeword to the English Edition1The Taming of Chance11The Origin of Play32Games People Play63Microcosm - Macrocosm194Statistical Bead Games305Darwin and Molecules492Games in Time and Space676Structure, Pattern, Shape697Symmetry1038Metamorphoses of Order1313The Limits of the Game - The Limits of Humanity1739The Parable of the Physicists17510Of Self-Reproducing Automata and Thinking Machines17811"From One Make Ten..."19912Limited Space and Resources21613From Ecosystem to Industrial Society2364In the Realm of Ideas24914Popper's Three Worlds25115From Symbol to Language25916Memory and Complex Reality28317The Art of Asking the Right Question29818Playing with Beauty306List of References331Index339

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Book SynopsisOffers a systematic and detailed treatment of the numerical solution of Markov chains. This book explores various aspects of numerically computing solutions of Markov chains, especially when the state is huge. It examines many different numerical computing methods - direct, single-and multi-vector iterative, and projection methods.Trade Review"The book contains very rich material which is the result of long-term research in this field. No other book is known to the reviewer that treats this subject in such detail... The book excellently reflects the great experience that the author has in the theory of Markov chains, matrix algebra, numerics and informatics. He ... richly illustrates the book with numerous examples, flow-charts, pictures and even computer screen copies."--Mathematical ReviewsTable of Contents* Markov Chains * Direct Methods * Iterative Methods * Projection Methods * Block Hessenberg Matrices * Decompositional Methods * LI-Cyclic Markov Chains * Transient Solutions * Stochastic Automata Networks * Software

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Book SynopsisAimed at a diverse scientific audience, this book explains the theory underlying the classical statistical methods. It covers topics that include common probability distributions; sampling and the distribution of sampling statistics; confidence intervals, hypothesis testing, and the theory of tests; estimation; and more.Trade Review"Aimed at a diverse scientific audience, including physicists, astronomers, chemists, geologists, and economists, this book explains the theory underlying the classical statistical methods ...There are nearly one hundred problems (with answers) designed to bring out points in the text and to cover topics lightly outside the main line of development."--Zentralblatt fur Mathematik

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Book SynopsisHow does mathematics enable us to send pictures from space back to Earth? Where does the bell-shaped curve come from? Drawing on areas of mathematics from probability theory, number theory, and geometry, this work highlights how ideas, mostly from pure math, can answer these questions. It includes puzzles and problems of varying difficulty.Trade ReviewOne of Choice's Outstanding Academic Titles for 2004 "Keith Ball demonstrated that though math may not be laugh-out-loud hilarious, it is deeply and gloriously satisfying... Ball's style is pacy and informal, and he does far more than just show off polished results. This is math with the hood up and the engine running."--Ben Longstaff, New Scientist "A recreational math book with enough heft to give its intended audience a series of mental workouts, ranging from the rough equivalent of a stroll to the corner mailbox to a hard mile run. The writing style is open and engaging."--Choice "A gem... Each topic is taken up in a setting that immediately generates interest ... Ball's achievement is to have come up with a selection of topics which are fresh and unusual... It is a pleasure to report that the book is written in limpid, graceful, elegant English prose--nowadays a nearly vanished species."--Stacy G. Langton, MAA Online "The author's writing style is informal, inviting, and clear... This book gives a lively and carefully written treatment of a number of interesting topics... The range of topics is wide, so even the experienced mathematician may learn something new."--Harold R. Parks, Notices of the American Mathematical Society "[I]f you salivate at the thought of working those calculations, then run don't walk to the bookshop--for once they've produced a book just for you."--Peter Spitz, Popular ScienceTable of ContentsPreface xi Acknowledgements xiii Chapter One Shannon's Free Lunch 1 1.1 The ISBN Code 1 1.2 Binary Channels 5 1.3 The Hunt for Good Codes 7 1.4 Parity-Check Construction 11 1.5 Decoding a Hamming Code 13 1.6 The Free Lunch Made Precise 19 1.7 Further Reading 21 1.8 Solutions 22 Chapter Two Counting Dots 25 2.1 Introduction 25 2.2 Why Is Pick's Theorem True?27 2.3 An Interpretation 31 2.4 Pick's Theorem and Arithmetic 32 2.5 Further Reading 34 2.6 Solutions 35 Chapter Three Fermat's Little Theorem and Infinite Decimals 41 3.1 Introduction 41 3.2 The Prime Numbers 43 3.3 Decimal Expansions of Reciprocals of Primes 46 3.4 An Algebraic Description of the Period 48 3.5 The Period Is a Factor of p 150 3.6 Fermat's Little Theorem 55 3.7 Further Reading 56 3.8 Solutions 58 Chapter Four Strange Curves 63 4.1 Introduction 63 4.2 A Curve Constructed Using Tiles 65 4.3 Is the Curve Continuous? 70 4.4 Does the Curve Cover the Square? 71 4.5 Hilbert's Construction and Peano's Original 73 4.6 A Computer Program 75 4.7 A Gothic Frieze 76 4.8 Further Reading 79 4.9 Solutions 80 Chapter Five Shared Birthdays, Normal Bells 83 5.1 Introduction 83 5.2 What Chance of a Match? 84 5.3 How Many Matches? 89 5.4 How Many People Share? 91 5.5 The Bell-Shaped Curve 93 5.6 The Area under a Normal Curve 100 5.7 Further Reading 105 5.8 Solutions 106 Chapter Six Stirling Works 109 6.1 Introduction 109 6.2 A First Estimate for n 110 6.3 A Second Estimate for n 114 6.4 A Limiting Ratio 117 6.5 Stirling's Formula 122 6.6 Further Reading 124 6.7 Solutions 125 Chapter Seven Spare Change, Pools of Blood 127 7.1 Introduction 127 7.2 The Coin-Weighing Problem 128 7.3 Back to Blood 131 7.4 The Binary Protocol for a Rare Abnormality 134 7.5 A Refined Binary Protocol 139 7.6 An Eficiency Estimate Using Telephones 141 7.7 An Eficiency Estimate for Blood Pooling 144 7.8 A Precise Formula for the Binary Protocol 147 7.9 Further Reading 149 7.10 Solutions 151 Chapter Eight Fibonacci's Rabbits Revisited 153 8.1 Introduction 153 8.2 Fibonacci and the Golden Ratio 154 8.3 The Continued Fraction for the Golden Ratio 158 8.4 Best Approximations and the Fibonacci Hyperbola 161 8.5 Continued Fractions and Matrices 165 8.6 Skipping down the Fibonacci Numbers 169 8.7 The Prime Lucas Numbers 174 8.8 The Trace Problem 178 8.9 Further Reading 181 8.10 Solutions 182 Chapter Nine Chasing the Curve 189 9.1 Introduction 189 9.2 Approximation by Rational Functions 193 9.3 The Tangent 202 9.4 An Integral Formula 207 9.5 The Exponential 210 9.6 The Inverse Tangent 213 9.7 Further Reading 214 9.8 Solutions 215 Chapter Ten Rational and Irrational 219 10.1 Introduction 219 10.2 Fibonacci Revisited 220 10.3 The Square Root of d 223 10.4 The Box Principle 225 10.5 The Numbers e and p 230 10.6 The Irrationality of e 233 10.7 Euler's Argument 236 10.8 The Irrationality of p 238 10.9 Further Reading 242 10.10 Solutions 243 Index 247

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Book SynopsisMeta-analysis is a powerful statistical methodology for synthesizing research evidence across independent studies. This is the first comprehensive handbook of meta-analysis written specifically for ecologists and evolutionary biologists, and it provides an invaluable introduction for beginners as well as an up-to-date guide for experienced meta-anaTrade Review"[T]his is a comprehensive and up-to-date compendium of all relevant aspects for meta-analysis conduction in ecology, evolution, and related topics. Scientists from these areas who already have some knowledge on meta-analysis will find valuable guidance."--Daniela Vetter, Quarterly Review of BiologyTable of ContentsPreface xi SECTION I: Introduction & Planning 1.Place of Meta-analysis among Other Methods of Research Synthesis 3 Julia Koricheva & Jessica Gurevitch 2.The Procedure of Meta-analysis in a Nutshell 14 Isabelle M. Cote & Michael D. Jennions SECTION II : Initiating a Meta-analysis 3.First Steps in Beginning a Meta-analysis 27 Gavin B. Stewart, Isabelle M. Cote, Hannah R. Rothstein, & Peter S. Curtis 4.Gathering Data: Searching Literature & Selection Criteria 37 Isabelle M. Cote, Peter S. Curtis, Hannah R. Rothstein, & Gavin B. Stewart 5.Extraction & Critical Appraisal of Data 52 Peter S. Curtis, Kerrie Mengersen, Marc J. Lajeunesse, Hannah R. Rothstein, & Gavin B. Stewart 6.Effect Sizes: Conventional Choices & Calculations 61 Michael S. Rosenberg, Hannah R. Rothstein, & Jessica Gurevitch 7.Using Other Metrics of Effect Size in Meta-analysis 72 Kerrie Mengersen & Jessica Gurevitch SECTION III : Essential Analytic Models & Methods 8.Statistical Models & Approaches to Inference 89 Kerrie Mengersen, Christopher H. Schmid, Michael D. Jennions, & Jessica Gurevitch 9.Moment & Least-Squares Based Approaches to Meta-analytic Inference 108 Michael S. Rosenberg 10.Maximum Likelihood Approaches to Meta-analysis 125 Kerrie Mengersen & Christopher H. Schmid 11.Bayesian Meta-analysis 145 Christopher H. Schmid & Kerrie Mengersen 12.Software for Statistical Meta-analysis 174 Christopher H. Schmid, Gavin B. Stewart, Hannah R. Rothstein, Marc J. Lajeunesse, & Jessica Gurevitch SECTION IV: Statistical Issues & Problems 13.Recovering Missing or Partial Data from Studies: A Survey of Conversions & Imputations for Meta-analysis 195 Marc J. Lajeunesse 14.Publication & Related Biases 207 Michael D. Jennions, Christopher J. Lortie, Michael S. Rosenberg, & Hannah R. Rothstein 15.Temporal Trends in Effect Sizes: Causes, Detection, & Implications 237 Julia Koricheva, Michael D. Jennions, & Joseph Lau 16.Statistical Models for the Meta-analysis of Nonindependent Data 255 Kerrie Mengersen, Michael D. Jennions, & Christopher H. Schmid 17.Phylogenetic Nonindependence & Meta-analysis 284 Marc J. Lajeunesse, Michael S. Rosenberg, & Michael D. Jennions 18.Meta-analysis of Primary Data 300 Kerrie Mengersen, Jessica Gurevitch, & Christopher H. Schmid 19.Meta-analysis of Results from Multisite Studies 313 Jessica Gurevitch SECTION V: Presentation & Interpretation of Results 20.Quality St&ards for Research Syntheses 323 Hannah R. Rothstein, Christopher J. Lortie, Gavin B. Stewart, Julia Koricheva, & Jessica Gurevitch 21.Graphical Presentation of Results 339 Christopher J. Lortie, Joseph Lau, & Marc J. Lajeunesse 22.Power Statistics for Meta-analysis: Tests for Mean Effects & Homogeneity 348 Marc J. Lajeunesse 23.Role of Meta-analysis in Interpreting the Scientific Literature 364 Michael D. Jennions, Christopher J. Lortie, & Julia Koricheva 24.Using Meta-analysis to Test Ecological & Evolutionary Theory 381 Michael D. Jennions, Christopher J. Lortie, & Julia Koricheva SECTION VI: Contributions of Meta-analysis in Ecology & Evolution 25.History & Progress of Meta-analysis 407 Joseph Lau, Hannah R. Rothstein, & Gavin B. Stewart 26.Contributions of Meta-analysis to Conservation & Management 420 Isabelle M. Cote & Gavin B. Stewart 27.Conclusions: Past, Present, & Future of Meta-analysis in Ecology & Evolution 426 Jessica Gurevitch & Julia Koricheva Glossary 433 Frequently Asked Questions 441 References 447 List of Contributors 487 Subject Index 489

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Book SynopsisOffers a modern and authoritative treatment of the mathematical processes that underlie performance modeling. This book looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers.Trade Review"The book represents a valuable text for courses in statistics and stochastic processes, so it is strongly recommended to libraries."--Hassan S. Bakouch, Journal of Applied StatisticsTable of ContentsPreface and Acknowledgments xv PART I PROBABILITY 1 Chapter 1: Probability 3 1.1 Trials, Sample Spaces, and Events 3 1.2 Probability Axioms and Probability Space 9 1.3 Conditional Probability 12 1.4 Independent Events 15 1.5 Law of Total Probability 18 1.6 Bayes' Rule 20 1.7 Exercises 21 Chapter 2: Combinatorics--The Art of Counting 25 2.1 Permutations 25 2.2 Permutations with Replacements 26 2.3 Permutations without Replacement 27 2.4 Combinations without Replacement 29 2.5 Combinations with Replacements 31 2.6 Bernoulli (Independent) Trials 33 2.7 Exercises 36 Chapter 3: Random Variables and Distribution Functions 40 3.1 Discrete and Continuous Random Variables 40 3.2 The Probability Mass Function for a Discrete Random Variable 43 3.3 The Cumulative Distribution Function 46 3.4 The Probability Density Function for a Continuous Random Variable 51 3.5 Functions of a Random Variable 53 3.6 Conditioned Random Variables 58 3.7 Exercises 60 Chapter 4: Joint and Conditional Distributions 64 4.1 Joint Distributions 64 4.2 Joint Cumulative Distribution Functions 64 4.3 Joint Probability Mass Functions 68 4.4 Joint Probability Density Functions 71 4.5 Conditional Distributions 77 4.6 Convolutions and the Sum of Two Random Variables 80 4.7 Exercises 82 Chapter 5: Expectations and More 87 5.1 Definitions 87 5.2 Expectation of Functions and Joint Random Variables 92 5.3 Probability Generating Functions for Discrete Random Variables 100 5.4 Moment Generating Functions 103 5.5 Maxima and Minima of Independent Random Variables 108 5.6 Exercises 110 Chapter 6: Discrete Distribution Functions 115 6.1 The Discrete Uniform Distribution 115 6.2 The Bernoulli Distribution 116 6.3 The Binomial Distribution 117 6.4 Geometric and Negative Binomial Distributions 120 6.5 The Poisson Distribution 124 6.6 The Hypergeometric Distribution 127 6.7 The Multinomial Distribution 128 6.8 Exercises 130 Chapter 7: Continuous Distribution Functions 134 7.1 The Uniform Distribution 134 7.2 The Exponential Distribution 136 7.3 The Normal or Gaussian Distribution 141 7.4 The Gamma Distribution 145 7.5 Reliability Modeling and the Weibull Distribution 149 7.6 Phase-Type Distributions 155 7.6.1 The Erlang-2 Distribution 155 7.6.2 The Erlang-r Distribution 158 7.6.3 The Hypoexponential Distribution 162 7.6.4 The Hyperexponential Distribution 164 7.6.5 The Coxian Distribution 166 7.6.6 General Phase-Type Distributions 168 7.6.7 Fitting Phase-Type Distributions to Means and Variances 171 7.7 Exercises 176 Chapter 8: Bounds and Limit Theorems 180 8.1 The Markov Inequality 180 8.2 The Chebychev Inequality 181 8.3 The Chernoff Bound 182 8.4 The Laws of Large Numbers 182 8.5 The Central Limit Theorem 184 8.6 Exercises 187 PART II MARKOV CHAINS 191 Chapter 9: Discrete- and Continuous-Time Markov Chains 193 9.1 Stochastic Processes and Markov Chains 193 9.2 Discrete-Time Markov Chains: Definitions 195 9.3 The Chapman-Kolmogorov Equations 202 9.4 Classification of States 206 9.5 Irreducibility 214 9.6 The Potential, Fundamental, and Reachability Matrices 218 9.6.1 Potential and Fundamental Matrices and Mean Time to Absorption 219 9.6.2 The Reachability Matrix and Absorption Probabilities 223 9.7 Random Walk Problems 228 9.8 Probability Distributions 235 9.9 Reversibility 248 9.10 Continuous-Time Markov Chains 253 9.10.1 Transition Probabilities and Transition Rates 254 9.10.2 The Chapman-Kolmogorov Equations 257 9.10.3 The Embedded Markov Chain and State Properties 259 9.10.4 Probability Distributions 262 9.10.5 Reversibility 265 9.11 Semi-Markov Processes 265 9.12 Renewal Processes 267 9.13 Exercises 275 Chapter 10: Numerical Solution of Markov Chains 285 10.1 Introduction 285 10.1.1 Setting the Stage 285 10.1.2 Stochastic Matrices 287 10.1.3 The Effect of Discretization 289 10.2 Direct Methods for Stationary Distributions 290 10.2.1 Iterative versus Direct Solution Methods 290 10.2.2 Gaussian Elimination and LU Factorizations 291 10.3 Basic Iterative Methods for Stationary Distributions 301 10.3.1 The Power Method 301 10.3.2 The Iterative Methods of Jacobi and Gauss-Seidel 305 10.3.3 The Method of Successive Overrelaxation 311 10.3.4 Data Structures for Large Sparse Matrices 313 10.3.5 Initial Approximations, Normalization, and Convergence 316 10.4 Block Iterative Methods 319 10.5 Decomposition and Aggregation Methods 324 10.6 The Matrix Geometric/Analytic Methods for Structured Markov Chains 332 10.6.1 The Quasi-Birth-Death Case 333 10.6.2 Block Lower Hessenberg Markov Chains 340 10.6.3 Block Upper Hessenberg Markov Chains 345 10.7 Transient Distributions 354 10.7.1 Matrix Scaling and Powering Methods for Small State Spaces 357 10.7.2 The Uniformization Method for Large State Spaces 361 10.7.3 Ordinary Differential Equation Solvers 365 10.8 Exercises 375 PART III QUEUEING MODELS 383 Chapter 11: Elementary Queueing Theory 385 11.1 Introduction and Basic Definitions 385 11.1.1 Arrivals and Service 386 11.1.2 Scheduling Disciplines 395 11.1.3 Kendall's Notation 396 11.1.4 Graphical Representations of Queues 397 11.1.5 Performance Measures--Measures of Effectiveness 398 11.1.6 Little's Law 400 11.2 Birth-Death Processes: The M/M/1 Queue 402 11.2.1 Description and Steady-State Solution 402 11.2.2 Performance Measures 406 11.2.3 Transient Behavior 412 11.3 General Birth-Death Processes 413 11.3.1 Derivation of the State Equations 413 11.3.2 Steady-State Solution 415 11.4 Multiserver Systems 419 11.4.1 The M/M/c Queue 419 11.4.2 The M/M/?Queue 425 11.5 Finite-Capacity Systems--The M/M/1/K Queue 425 11.6 Multiserver, Finite-Capacity Systems--The M/M/c/K Queue 432 11.7 Finite-Source Systems--The M/M/c//M Queue 434 11.8 State-Dependent Service 437 11.9 Exercises 438 Chapter 12: Queues with Phase-Type Laws: Neuts' Matrix-Geometric Method 444 12.1 The Erlang-r Service Model--The M/Er/1 Queue 444 12.2 The Erlang-r Arrival Model--The Er/M/1 Queue 450 12.3 The M/H2/1 and H2/M/1 Queues 454 12.4 Automating the Analysis of Single-Server Phase-Type Queues 458 12.5 The H2/E3/1 Queue and General Ph/Ph/1 Queues 460 12.6 Stability Results for Ph/Ph/1 Queues 466 12.7 Performance Measures for Ph/Ph/1 Queues 468 12.8 Matlab code for Ph/Ph/1 Queues 469 12.9 Exercises 471 Chapter 13: The z-Transform Approach to Solving Markovian Queues 475 13.1 The z-Transform 475 13.2 The Inversion Process 478 13.3 Solving Markovian Queues using z-Transforms 484 13.3.1 The z-Transform Procedure 484 13.3.2 The M/M/1 Queue Solved using z-Transforms 484 13.3.3 The M/M/1 Queue with Arrivals in Pairs 486 13.3.4 The M/Er/1 Queue Solved using z-Transforms 488 13.3.5 The Er/M/1 Queue Solved using z-Transforms 496 13.3.6 Bulk Queueing Systems 503 13.4 Exercises 506 Chapter 14: The M/G/1 and G/M/1 Queues 509 14.1 Introduction to the M/G/1 Queue 509 14.2 Solution via an Embedded Markov Chain 510 14.3 Performance Measures for the M/G/1 Queue 515 14.3.1 The Pollaczek-Khintchine Mean Value Formula 515 14.3.2 The Pollaczek-Khintchine Transform Equations 518 14.4 The M/G/1 Residual Time: Remaining Service Time 523 14.5 The M/G/1 Busy Period 526 14.6 Priority Scheduling 531 14.6.1 M/M/1: Priority Queue with Two Customer Classes 531 14.6.2 M/G/1: Nonpreemptive Priority Scheduling 533 14.6.3 M/G/1: Preempt-Resume Priority Scheduling 536 14.6.4 A Conservation Law and SPTF Scheduling 538 14.7 The M/G/1/K Queue 542 14.8 The G/M/1 Queue 546 14.9 The G/M/1/K Queue 551 14.10 Exercises 553 Chapter 15: Queueing Networks 559 15.1 Introduction 559 15.1.1 Basic Definitions 559 15.1.2 The Departure Process--Burke's Theorem 560 15.1.3 Two M/M/1 Queues in Tandem 562 15.2 Open Queueing Networks 563 15.2.1 Feedforward Networks 563 15.2.2 Jackson Networks 563 15.2.3 Performance Measures for Jackson Networks 567 15.3 Closed Queueing Networks 568 15.3.1 Definitions 568 15.3.2 Computation of the Normalization Constant: Buzen's Algorithm 570 15.3.3 Performance Measures 577 15.4 Mean Value Analysis for Closed Queueing Networks 582 15.5 The Flow-Equivalent Server Method 591 15.6 Multiclass Queueing Networks and the BCMP Theorem 594 15.6.1 Product-Form Queueing Networks 595 15.6.2 The BCMP Theorem for Open, Closed, and Mixed Queueing Networks 598 15.7 Java Code 602 15.8 Exercises 607 PART IV SIMULATION 611 Chapter 16: Some Probabilistic and Deterministic Applications of Random Numbers 613 16.1 Simulating Basic Probability Scenarios 613 16.2 Simulating Conditional Probabilities, Means, and Variances 618 16.3 The Computation of Definite Integrals 620 16.4 Exercises 623 Chapter 17: Uniformly Distributed "Random" Numbers 625 17.1 Linear Recurrence Methods 626 17.2 Validating Sequences of Random Numbers 630 17.2.1 The Chi-Square "Goodness-of-Fit" Test 630 17.2.2 The Kolmogorov-Smirnov Test 633 17.2.3 "Run" Tests 634 17.2.4 The "Gap" Test 640 17.2.5 The "Poker" Test 641 17.2.6 Statistical Test Suites 644 17.3 Exercises 644 Chapter 18: Nonuniformly Distributed "Random" Numbers 647 18.1 The Inverse Transformation Method 647 18.1.1 The Continuous Uniform Distribution 649 18.1.2 "Wedge-Shaped" Density Functions 649 18.1.3 "Triangular" Density Functions 650 18.1.4 The Exponential Distribution 652 18.1.5 The Bernoulli Distribution 653 18.1.6 An Arbitrary Discrete Distribution 653 18.2 Discrete Random Variates by Mimicry 654 18.2.1 The Binomial Distribution 654 18.2.2 The Geometric Distribution 655 18.2.3 The Poisson Distribution 656 18.3 The Accept-Reject Method 657 18.3.1 The Lognormal Distribution 660 18.4 The Composition Method 662 18.4.1 The Erlang-r Distribution 662 18.4.2 The Hyperexponential Distribution 663 18.4.3 Partitioning of the Density Function 664 18.5 Normally Distributed Random Numbers 670 18.5.1 Normal Variates via the Central Limit Theorem 670 18.5.2 Normal Variates via Accept-Reject and Exponential Bounding Function 670 18.5.3 Normal Variates via Polar Coordinates 672 18.5.4 Normal Variates via Partitioning of the Density Function 673 18.6 The Ziggurat Method 673 18.7 Exercises 676 Chapter 19: Implementing Discrete-Event Simulations 680 19.1 The Structure of a Simulation Model 680 19.2 Some Common Simulation Examples 682 19.2.1 Simulating the M/M/1 Queue and Some Extensions 682 19.2.2 Simulating Closed Networks of Queues 686 19.2.3 The Machine Repairman Problem 689 19.2.4 Simulating an Inventory Problem 692 19.3 Programming Projects 695 Chapter 20: Simulation Measurements and Accuracy 697 20.1 Sampling 697 20.1.1 Point Estimators 698 20.1.2 Interval Estimators/Confidence Intervals 704 20.2 Simulation and the Independence Criteria 707 20.3 Variance Reduction Methods 711 20.3.1 Antithetic Variables 711 20.3.2 Control Variables 713 20.4 Exercises 716 Appendix A: The Greek Alphabet 719 Appendix B: Elements of Linear Algebra 721 B.1 Vectors and Matrices 721 B.2 Arithmetic on Matrices 721 B.3 Vector and Matrix Norms 723 B.4 Vector Spaces 724 B.5 Determinants 726 B.6 Systems of Linear Equations 728 B.6.1 Gaussian Elimination and LU Decompositions 730 B.7 Eigenvalues and Eigenvectors 734 B.8 Eigenproperties of Decomposable, Nearly Decomposable, and Cyclic Stochastic Matrices 738 B.8.1 Normal Form 738 B.8.2 Eigenvalues of Decomposable Stochastic Matrices 739 B.8.3 Eigenvectors of Decomposable Stochastic Matrices 741 B.8.4 Nearly Decomposable Stochastic Matrices 743 B.8.5 Cyclic Stochastic Matrices 744 Bibliography 745 Index 749

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Book SynopsisBenford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together maTrade Review"This book will prove to be both a valuable reference and a first source to turn to for whoever is interested in the mathematical genesis and empirical usefulness of Benford's law."--Walter Kramer, Statistical PapersTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. xiii*Preface, pg. xvii*Notation, pg. xxiii*Chapter One. A Quick Introduction to Benford's Law, pg. 3*Chapter Two. A Short Introduction to the Mathematical Theory of Benford's Law, pg. 23*Chapter Three. Fourier Analysis and Benford's Law, pg. 68*Chapter Four. Benford's Law Geometry, pg. 109*Chapter Five. Explicit Error Bounds via Total Variation, pg. 119*Chapter Six. Levy Processes and Benford's Law, pg. 135*Chapter Seven. Benford's Law as a Bridge between Statistics and Accounting, pg. 177*Chapter Eight. Detecting Fraud and Errors Using Benford's Law, pg. 191*Chapter Nine. Can Vote Counts' Digits and Benford's Law Diagnose Elections?, pg. 212*Chapter Ten. Complementing Benford's Law for Small N: A Local Bootstrap, pg. 223*Chapter Eleven. Measuring the Quality of European Statistics, pg. 235*Chapter Twelve. Benford's Law and Fraud in Economic Research, pg. 244*Chapter Thirteen. Testing for Strategic Manipulation of Economic and Financial Data, pg. 257*Chapter Fourteen. Psychology and Benford's Law, pg. 267*Chapter Fifteen. Managing Risk in Numbers Games, pg. 276*Chapter Sixteen. Benford's Law in the Natural Sciences, pg. 290*Chapter Seventeen. Generalizing Benford's Law, pg. 304*Chapter Eighteen. PV Modeling of Medical Imaging Systems, pg. 319*Chapter Nineteen. Application of Benford's Law to Images, pg. 338*Chapter Twenty. Exercises, pg. 373*Bibliography, pg. 402*Index, pg. 433

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Book SynopsisTrade Review"I recommend the book to everyone who is studying and fascinated by statistics."---Singalakha Menziwa, Mathemafrica"Steven J. Miller’s The Probability Lifesaver presents, as its subtitle claims, 'all the tools you need to understand chance' in a clear, straightforward manner. . . . For the students that have a good understanding of Calculus, the combination of the probability discussions along with the calculus behind these topics is very beneficial." * MAA Reviews *"The breadth of the book’s coverage and its clear, informal tone in addressing highly formal problems remind one of a friendly professor offering unlimited office hours, and the book will be a highly accessible supplement for students working through another, more conventional text. . . . [This is] a volume that deserves to be widely known in educational circles and will likely find its way to the shelves of practicing statisticians who wish to probe below the surface of fundamental theorems that they have learned by rote."---H. Van Dyke Parunak, Computing Reviews

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Book SynopsisWhenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly - why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion - how is this possible? This title includes some of these counterintuitive mathematical occurrences.Trade Review"Havil once again explores a variety of mathematical results and problems that at first appear to be self-contradictory, or stated in such a way that no solution could exist. In each case, he then either sketches a proof of why the result is not contradictory, or explains the solution to the seemingly unsolvable problem ... Like a magician revealing secrets, Havil maintains this sense through most chapters, dropping the punch line at just the right moment."--J.T. Noonan, Choice "This sequel to the author's book Nonplussed! supplies another set of brain-stretching problems and ideas. Its subtitle is 'Surprising Solutions to Counterintuitive Conundrums'; the surprise often consisting of the fact that it is possible to obtain a solution at all! ... This is another excellent book by Havil, following in the Martin Gardner tradition."--Alan Stevens, Mathematics Today "Julian Havil has quietly joined the ranks of the very best writers of popular mathematics. His two volume set Impossible? and Nonplussed! Mathematical Proof of Implausible Ideas not only belong in every library, but in the hands of every young person interested in mathematics and especially in the hands of their teachers."--John J. Watkins, Mathematical Intelligencer "Impossible? is an immensely thought-provoking book. Even if you skim or skip the more complex abstract math, you may have a hard time letting these puzzles go, so strongly do they flout common sense. You'll just have to do your best to put them our of your mind when you need to get some sleep, but if the situation ever arises, be sure to take Monty up on his offer."--Ray Bert, Civil Engineering "I would highly recommend this book as a reference for the mathematician who likes recreational mathematics, or as a good read for the recreational enthusiast with a penchant for more rigor."--Blair Madore, MAA ReviewsTable of ContentsAcknowledgments xi Introduction 1 Chapter 1: It's Common Knowledge 3 Chapter 2: Simpson's Paradox 11 Chapter 3: The Impossible Problem 21 Chapter 4: Braess's Paradox 31 Chapter 5: The Power of Complex Numbers 39 Chapter 6: Bucking the Odds 50 Chapter 7: Cantor's Paradise 68 Chapter 8: Gamow-Stern Elevators 82 Chapter 9: The Toss of a Coin 88 Chapter 10: Wild-Card Poker 103 Chapter 11: Two Series 113 Chapter 12: Two Card Tricks 131 Chapter 13: The Spin of a Needle 146 Chapter 14: The Best Choice 165 Chapter 15: The Power of Powers 176 Chapter 16: Benford's Law 190 Chapter 17: Goodstein Sequences 201 Chapter 18: The Banach-Tarski Paradox 210 The Motifs 217 Appendix 221 Index 233

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Book SynopsisExplores a range of entertaining questions about urban life such as: How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? And, more.Trade Review"[Adam's] writing is fun and accessible... College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."--Library Journal "For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice "Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"--Sandra L. Arlinghaus, Mathematical Reviews Clippings "It goes without saying that the exposition is very friendly and lucid: this makes the vast majority of material accessible to a general audience interested in mathematical modeling and real life applications. This excellent book may well complement standard texts on engineering mathematics, mathematical modeling, applied mathematics, differential equations; it is a delightful and entertaining reading itself. Thank you, Vickie Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam--your idea has been delightfully implemented!"--Svitlana P. Rogovchenko, Zentralblatt MATH "[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be... A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."--David S. Mazel, MAA Reviews "The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."--Theresa Jorgensen, Mathematics TeacherTable of ContentsPreface xiii Acknowledgments xvii Chapter 1 Introduction: Cancer, Princess Dido, and the city 1 Chapter 2 Getting to the city 7 Chapter 3 Living in the city 15 Chapter 4 Eating in the city 35 Chapter 5 Gardening in the city 41 Chapter 6 Summer in the city 47 Chapter 7 Not driving in the city! 63 Chapter 8 Driving in the city 73 Chapter 9 Probability in the city 89 Chapter 10 Traffic in the city 97 Chapter 11 Car following in the city--I 107 Chapter 12 Car following in the city--II 113 Chapter 13 Congestion in the city 121 Chapter 14 Roads in the city 129 Chapter 15 Sex and the city 135 Chapter 16 Growth and the city 149 Chapter 17 The axiomatic city 159 Chapter 18 Scaling in the city 167 Chapter 19 Air pollution in the city 179 Chapter 20 Light in the city 191 Chapter 21 Nighttime in the city--I 209 Chapter 22 Nighttime in the city--II 221 Chapter 23 Lighthouses in the city? 233 Chapter 24 Disaster in the city? 247 Chapter 25 Getting away from the city 255 Appendix 1 Theorems for Princess Dido 261 Appendix 2 Dido and the sinc function 263 Appendix 3 Taxicab geometry 269 Appendix 4 The Poisson distribution 273 Appendix 5 The method of Lagrange multipliers 277 Appendix 6 A spiral braking path 279 Appendix 7 The average distance between two random points in a circle 281 Appendix 8 Informal "derivation" of the logistic differential equation 283 Appendix 9 A miniscule introduction to fractals 287 Appendix 10 Random walks and the diffusion equation 291 Appendix 11 Rainbow/halo details 297 Appendix 12 The Earth as vacuum cleaner? 303 Annotated references and notes 309 Index 317

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Book SynopsisWhat are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. This title challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations.Trade Review"Nahin's sophisticated puzzles, and their accompanying explanations, have a far better than even chance of fascinating and preoccupying the mathematically literate readership they seek."--Publisher's Weekly "An entertaining, thought-provoking collection of twenty-one puzzles...These puzzles invite the reader to think intuitively, mathematically, and creatively about the laws of probability as they apply in lighthearted, often counterintuitive ways to a diverse collection of practical and speculative situations."--Mathematics Teacher "By following Nahin's informal style it is possible to set [the examples] up quickly from first principles and slip them into courses on calculus, algebra, or scientific programming. They also offer a wealth of topics for undergraduate projects. Those duelling idiots are fighting over a goldmine."--Des Higham, MSOR ConnectionsTable of ContentsAcknowledgments ix Preface xi Introduction 3 The Problems 15 1. How to ask an Embarrassing question 15 2. When Idiots duel 16 3. Will the light Bulb glow? 22 4. Tho Underdog and the World Series 26 5. The Curious Case of the Snowy Birthdays 27 6. When Human Flesh Begins to Fail 34 7. Baseball Again, and Mortal Flesh Too 51 8. Ball Madness 56 9. Who Pays for the Coffee? 42 10. The Chess Champ versus the Gunslinger 45 11. A Different Slice of Probabilistic Pi 49 12. When Negativity is a No-No 50 15. The Power of Randomness 51 14. The Random Radio 52 15. An Inconceivable Difficulty 55 16. The Unsinkable Tub is Sinking! How to Find Her, Fast 57 17. A Walk in the Garden 58 18. Two Flies Stuck on a Piece of Flypaper--How Far Apart? 61 19.The Blind Spider and the Fly 62 20. Reliably Unreliable 68 21. When Theory Fails, There is always the Computer 71 The Solutions 81 Random Number Generators 176 "Some things Just Have to be Done By Hand!" 198 MATLAB Programs 202 Index 267 About the Author 271

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Book SynopsisSome probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to geTrade Review"The problems are accessible but still realistic enough to be engaging, and the solutions in the back of the book will get you through any sticky spots. Writing your own versions of a few of these programs will acquaint you with a useful approach to problem solving and a novel style of thinking."--Brian Hayes, American Scientist "Digital Dice will appeal to recreational mathematicians who have even a limited knowledge of computer programming, and even nonprogrammers will find most of the problems entertaining to ponder."--Games Magazine "[An] enjoyable read, as [Nahin] writes clearly, with humour and is not afraid to include equations where necessary. Nahin spices the book throughout with factual and anecdotal snippets. Digital Dice will appeal to all who like recreational mathematics."--Alan Stevens, Mathematics Today "[T]he book is targeted at teachers and students of probability theory or computer science, as well as aficionados of recreational mathematics, but anyone who is familiar with the basics of probability and is capable of writing simple computer programs will have no problem working their way through this interesting and rewarding book."--Physics World "After the appearance of the author's earlier book on probability problems, [Duelling Idiots And Other Probability Puzzlers], one has high expectations for this book, and one is not disappointed... The book will certainly have great appeal to all three of the targeted audiences."--G A. Hewer, Mathematical Reviews "This well-written entertaining collection of twenty-one probability problems presents their origin and history as well as their computer solutions... These problems could be used in a computer programming course or a probability course that includes Monte Carlo simulations."--Thomas Sonnabend, Mathematics Teacher "All of the books by Nahin and Havil are worth having, including others not listed here. I particularly recommend Digital Dice for the task of teaching undergraduates in mathematics the fundamentals of computation and simulation."--James M. Cargal, The UMAP JournalTable of ContentsPreface to the Paperback Edition xiii Introduction 1 The Problems 35 1. The Clumsy Dishwasher Problem 37 2. Will Lil and Bill Meet at the Malt Shop? 38 3. A Parallel Parking Question 40 4. A Curious Coin-Flipping Game 42 5. The Gamow-Stern Elevator Puzzle 45 6. Steve's Elevator Problem 48 7. The Pipe Smoker's Discovery 51 8. A Toilet Paper Dilemma 53 9. The Forgetful Burglar Problem 59 10. The Umbrella Quandary 61 11. The Case of the Missing Senators 63 12. How Many Runners in a Marathon? 65 13. A Police Patrol Problem 69 14. Parrondo's Paradox 74 15. How Long Is the Wait to Get the Potato Salad? 77 16. The Appeals Court Paradox 81 17. Waiting for Buses 83 18. Waiting for Stoplights 85 19. Electing Emperors and Popes 87 20. An Optimal Stopping Problem 91 21. Chain Reactions, Branching Processes, and Baby Boys 96 MATLAB Solutions To The Problems 101 1. The Clumsy Dishwasher Problem 103 2. Will Lil and Bill Meet at the Malt Shop? 105 3. A Parallel Parking Question 109 4. A Curious Coin-Flipping Game 114 5. The Gamow-Stern Elevator Puzzle 120 6. Steve's Elevator Problem 124 7. The Pipe Smoker's Discovery 129 8. A Toilet Paper Dilemma 140 9. The Forgetful Burglar Problem 144 10. The Umbrella Quandary 148 11. The Case of the Missing Senators 153 12. How Many Runners in a Marathon? 157 13. A Police Patrol Problem 160 14. Parrondo's Paradox 169 15. How Long is the Wait to Get the Potato Salad? 176 16. The Appeals Court Paradox 184 17. Waiting for Buses 187 18. Waiting for Stoplights 191 19. Electing Emperors and Popes 197 20. An Optimal Stopping Problem 204 21. Chain Reactions, Branching Processes, and Baby Boys 213 Appendix 1. One Way to Guess on a Test 221 Appendix 2. An Example of Variance-Reduction in the Monte Carlo Method 223 Appendix 3. Random Harmonic Sums 229 Appendix 4. Solving Montmort's Problem by Recursion 231 Appendix 5. An Illustration of the Inclusion-Exclusion Principle 237 Appendix 6. Solutions to the Spin Game 244 Appendix 7. How to Simulate Kelvin's Fair Coin with a Biased Coin 248 Appendix 8. How to Simulate an Exponential Random Variable 252 Appendix 9. Index to Author-Created MATLAB m-Files in the Book 255 Glossary 257 Acknowledgments 259 Index 261 Also by Paul J. Nahin 265

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Book SynopsisA website's ranking on Google can spell the difference between success and failure for a new business. NCAA football ratings determine which schools get to play for the big money in postseason bowl games. Product ratings influence everything from the clothes we wear to the movies we select on Netflix. Ratings and rankings are everywhere, but how exTrade Review"[A] thorough exploration of the methods and applications of ranking for an audience ranging from computer scientists and engineers to high-school teachers to 'people interested in wagering on just about anything'."--Nature Physics "Who's #1 provides a fascinating tour through the world of rankings and is highly recommended."--Richard J. Wilders, MAA Reviews "[T]he book ... provide[s] an excellent, accessible, and stimulating discussion of the material it does cover. Overall, the book makes a valuable addition to the canon of rating and ranking."--David J. Hand, Journal of Applied Statistics "This book provides an interesting overview of ranking various sports teams, chess players, politicians, and the like in real-life circumstances, which typically involve serious constraints on the time available to find the optimal ranking."--Choice "The book could be used to supplement a course on linear algebra and/or numerical linear algebra... The book could also be used as the basis for a short topics course or undergraduate research project on ranking, or it could be used in a modeling class as an example of how mathematical modeling is done. In addition to describing the mathematics of ranking, the book is full of interesting tidbits that add to the pleasure of its reading."--James Keener, SIAM Review "When I started this book I knew very little about American football. I was little the wiser after finishing it, but I had an excellent understanding of various methods used in the obtaining of the ranking of teams and their interrelationships. Langville and Meyer are to be commended for this collection, and anyone who is more conversant with North American sports than I am will most certainly be stimulated by reading Who's #1?"--Andrew I. Dale, Notices of the AMS "Readers will find many interesting ideas as they grapple with the complexities of the science of rating and ranking."--Bob Horton, Mathematics Teacher "[T]his book is a call to consciousness on the relevance of rating and ranking as well as an enjoyable start-up guide from the point of view of algebraic methods."--Francisco Grimaldo Moreno, JASSS "This book is a great introduction to the field (including its constituent parts in linear algebra and data mining) and contains enough depth to be used as a supplemental book in a data mining course or as a jumping off point for an interested researcher... Overall this is a very nice, well written book that could be use in multiple ways by a wide variety of audiences."--Nicholas Mattei, SigAct News "The profit the scientometrics community can gain from this book is an indirect one: an attitude how to compile a systematic collection of potential methods, how to select carefully using theoretical tests and empirical examples and how to combine methods to get a comprehensive, multidimensional rating and ranking system. In this sense, it is a highly recommended reading for all readers of the journal Scientometrics."--Andras Schubert, Scientometrics "This book is an excellent read for everyone; readers might be sports enthusiasts, social choice theorists, mathematicians, computer scientists, engineers, and college and high school teachers. Teachers will find quite an easy way to extract material for a short module."--Valentina Dagiene, Zentralblatt MATHTable of ContentsPreface xiii Purpose xiii Audience xiii Prerequisites xiii Teaching from This Book xiv Acknowledgments xiv Chapter 1. Introduction to Ranking 1 Social Choice and Arrow's Impossibility Theorem 3 Arrow's Impossibility Theorem 4 Small Running Example 4 Chapter 2. Massey's Method 9 Initial Massey Rating Method 9 Massey's Main Idea 9 The Running Example Using the Massey Rating Method 11 Advanced Features of the Massey Rating Method 11 The Running Example: Advanced Massey Rating Method 12 Summary of the Massey Rating Method 13 Chapter 3. Colley's Method 21 The Running Example 23 Summary of the Colley Rating Method 24 Connection between Massey and Colley Methods 24 Chapter 4. Keener's Method 29 Strength and Rating Stipulations 29 Selecting Strength Attributes 29 Laplace's Rule of Succession 30 To Skew or Not to Skew? 31 Normalization 32 Chicken or Egg? 33 Ratings 33 Strength 33 The Keystone Equation 34 Constraints 35 Perron-Frobenius 36 Important Properties 37 Computing the Ratings Vector 37 Forcing Irreducibility and Primitivity 39 Summary 40 The 2009-2010 NFL Season 42 Jim Keener vs. Bill James 45 Back to the Future 48 Can Keener Make You Rich? 49 Conclusion 50 Chapter 5. Elo's System 53 Elegant Wisdom 55 The K-Factor 55 The Logistic Parameter ? 56 Constant Sums 56 Elo in the NFL 57 Hindsight Accuracy 58 Foresight Accuracy 59 Incorporating Game Scores 59 Hindsight and Foresight with ? = 1000, K = 32, H = 15 60 Using Variable K-Factors with NFL Scores 60 Hindsight and Foresight Using Scores and Variable K-Factors 62 Game-by-Game Analysis 62 Conclusion 64 Chapter 6. The Markov Method 67 The Markov Method 67 Voting with Losses 68 Losers Vote with Point Differentials 69 Winners and Losers Vote with Points 70 Beyond Game Scores 71 Handling Undefeated Teams 73 Summary of the Markov Rating Method 75 Connection between the Markov and Massey Methods 76 Chapter 7. The Offense-Defense Rating Method 79 OD Objective 79 OD Premise 79 But Which Comes First? 80 Alternating Refinement Process 81 The Divorce 81 Combining the OD Ratings 82 Our Recurring Example 82 Scoring vs. Yardage 83 The 2009-2010 NFL OD Ratings 84 Mathematical Analysis of the OD Method 87 Diagonals 88 Sinkhorn-Knopp 89 OD Matrices 89 The OD Ratings and Sinkhorn-Knopp 90 Cheating a Bit 91 Chapter 8. Ranking by Reordering Methods 97 Rank Differentials 98 The Running Example 99 Solving the Optimization Problem 101 The Relaxed Problem 103 An Evolutionary Approach 103 Advanced Rank-Differential Models 105 Summary of the Rank-Differential Method 106 Properties of the Rank-Differential Method 106 Rating Differentials 107 The Running Example 109 Solving the Reordering Problem 110 Summary of the Rating-Differential Method 111 Chapter 9. Point Spreads 113 What It Is (and Isn't) 113 The Vig (or Juice) 114 Why Not Just Offer Odds? 114 How Spread Betting Works 114 Beating the Spread 115 Over/Under Betting 115 Why Is It Difficult for Ratings to Predict Spreads? 116 Using Spreads to Build Ratings (to Predict Spreads?) 117 NFL 2009-2010 Spread Ratings 120 Some Shootouts 121 Other Pair-wise Comparisons 124 Conclusion 125 Chapter 10. User Preference Ratings 127 Direct Comparisons 129 Direct Comparisons, Preference Graphs, and Markov Chains 130 Centroids vs. Markov Chains 132 Conclusion 133 Chapter 11. Handling Ties 135 Input Ties vs. Output Ties 136 Incorporating Ties 136 The Colley Method 136 The Massey Method 137 The Markov Method 137 The OD, Keener, and Elo Methods 138 Theoretical Results from Perturbation Analysis 139 Results from Real Datasets 140 Ranking Movies 140 Ranking NHL Hockey Teams 141 Induced Ties 142 Summary 144 Chapter 12. Incorporating Weights 147 Four Basic Weighting Schemes 147 Weighted Massey 149 Weighted Colley 150 Weighted Keener 150 Weighted Elo 150 Weighted Markov 150 Weighted OD 151 Weighted Differential Methods 151 Chapter 13. "What If ..." Scenarios and Sensitivity 155 The Impact of a Rank-One Update 155 Sensitivity 156 Chapter 14. Rank Aggregation-Part 1 159 Arrow's Criteria Revisited 160 Rank-Aggregation Methods 163 Borda Count 165 Average Rank 166 Simulated Game Data 167 Graph Theory Method of Rank Aggregation 172 A Refinement Step after Rank Aggregation 175 Rating Aggregation 176 Producing Rating Vectors from Rating Aggregation-Matrices 178 Summary of Aggregation Methods 181 Chapter 15. Rank Aggregation-Part 2 183 The Running Example 185 Solving the BILP 186 Multiple Optimal Solutions for the BILP 187 The LP Relaxation of the BILP 188 Constraint Relaxation 190 Sensitivity Analysis 191 Bounding 191 Summary of the Rank-Aggregation (by Optimization) Method 193 Revisiting the Rating-Differential Method 194 Rating Differential vs. Rank Aggregation 194 The Running Example 196 Chapter 16. Methods of Comparison 201 Qualitative Deviation between Two Ranked Lists 201 Kendall's Tau 203 Kendall's Tau on Full Lists 204 Kendall's Tau on Partial Lists 205 Spearman's Weighted Footrule on Full Lists 206 Spearman's Weighted Footrule on Partial Lists 207 Partial Lists of Varying Length 210 Yardsticks: Comparing to a Known Standard 211 Yardsticks: Comparing to an Aggregated List 211 Retroactive Scoring 212 Future Predictions 212 Learning Curve 214 Distance to Hillside Form 214 Chapter 17. Data 217 Massey's Sports Data Server 217 Pomeroy's College Basketball Data 218 Scraping Your Own Data 218 Creating Pair-wise Comparison Matrices 220 Chapter 18. Epilogue 223 Analytic Hierarchy Process (AHP) 223 The Redmond Method 223 The Park-Newman Method 224 Logistic Regression/Markov Chain Method (LRMC) 224 Hochbaum Methods 224 Monte Carlo Simulations 224 Hard Core Statistical Analysis 225 And So Many Others 225 Glossary 231 Bibliography 235 Index 241

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Book SynopsisX and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow throughTrade Review"[Adam's] writing is fun and accessible... College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."--Library Journal "For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice "Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"--Sandra L. Arlinghaus, Mathematical Reviews Clippings "It goes without saying that the exposition is very friendly and lucid: this makes the vast majority of material accessible to a general audience interested in mathematical modeling and real life applications. This excellent book may well complement standard texts on engineering mathematics, mathematical modeling, applied mathematics, differential equations; it is a delightful and entertaining reading itself. Thank you, Vickie Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam--your idea has been delightfully implemented!"--Svitlana P. Rogovchenko, Zentralblatt MATH "[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be... A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."--David S. Mazel, MAA Reviews "The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."--Theresa Jorgensen, Mathematics TeacherTable of ContentsPreface xiii Acknowledgments xvii Chapter 1 Introduction: Cancer, Princess Dido, and the city 1 Chapter 2 Getting to the city 7 Chapter 3 Living in the city 15 Chapter 4 Eating in the city 35 Chapter 5 Gardening in the city 41 Chapter 6 Summer in the city 47 Chapter 7 Not driving in the city! 63 Chapter 8 Driving in the city 73 Chapter 9 Probability in the city 89 Chapter 10 Traffic in the city 97 Chapter 11 Car following in the city--I 107 Chapter 12 Car following in the city--II 113 Chapter 13 Congestion in the city 121 Chapter 14 Roads in the city 129 Chapter 15 Sex and the city 135 Chapter 16 Growth and the city 149 Chapter 17 The axiomatic city 159 Chapter 18 Scaling in the city 167 Chapter 19 Air pollution in the city 179 Chapter 20 Light in the city 191 Chapter 21 Nighttime in the city--I 209 Chapter 22 Nighttime in the city--II 221 Chapter 23 Lighthouses in the city? 233 Chapter 24 Disaster in the city? 247 Chapter 25 Getting away from the city 255 Appendix 1 Theorems for Princess Dido 261 Appendix 2 Dido and the sinc function 263 Appendix 3 Taxicab geometry 269 Appendix 4 The Poisson distribution 273 Appendix 5 The method of Lagrange multipliers 277 Appendix 6 A spiral braking path 279 Appendix 7 The average distance between two random points in a circle 281 Appendix 8 Informal "derivation" of the logistic differential equation 283 Appendix 9 A miniscule introduction to fractals 287 Appendix 10 Random walks and the diffusion equation 291 Appendix 11 Rainbow/halo details 297 Appendix 12 The Earth as vacuum cleaner? 303 Annotated references and notes 309 Index 317

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Book SynopsisTrade Review"Winner of a SABR Baseball Research Award, Society for American Baseball Research""Finalist for the CASEY Award for Best Baseball Book of the Year, Spitball Magazine""The subject of Christopher Phillips’s Scouting and Scoring is baseball, but it’s worth reading for more than just the baseball. The book is an effort to help us understand one of the oldest problems in modern societies, which is how to evaluate human beings."---Louis Menand, New Yorker"Phillips’ book is an enticing read for baseball data enthusiasts and, more broadly, those interested in thinking about notions such as ‘fact’ and ‘truth,’ how one measures the seemingly immeasurable, and attempts to quantify human potential."---Russ Goodman, MAA Reviews

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Book SynopsisTrade Review"For graduate students and researchers who are interested in high-dimensional statistics and its interplay with convex optimization, this book will serve as an invaluable resource."---Debashis Ghosh, International Statistical Review

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Book Synopsis

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