Probability and statistics Books

Book SynopsisWith meta-analysis methods playing a crucial role in health research in recent years, this important and clearly-written book provides a much-needed survey of the field. Meta-analysis provides a framework for combining the results of several clinical trials and drawing inferences about the effectiveness of medical treatments.Trade Review“Both books can be recommended for graduate training and are useful additions to the library of those interested in the meta-analytic accumulation of literatures on training, vocational learning, and education in the professions.” (Vocations and Learning, 15 December 2010) "This well-written book offers an exhaustive criticism and up-to-date references, illustrates effectively with real life examples and data…" (Journal of Statistical Computation & Simulation, July 2004) "this is an excellent book..." (Short Book Reviews, April 2001) "...recommended for mathematically skilled readers interested in getting an overview of the various methods and the existing literature..." (Statistics in Medicine, 15 October 2003) Table of ContentsPART A: META-ANALYSIS METHODOLOGY: THE BASICS Introduction: Meta-analysis: Its Development and Uses Defining Outcome Measures used for Combining via Meta-analysis Random Effects Models for Combining Study Estimates Exploring Between Study Heterogeneity Publication Bias Study Quality Sensitivity Analysis Reporting the Results of a Meta-analysis Fixed Effects Methods for Combining Study Estimates PART B: ADVANCED AND SPECIALIZED META-ANALYSIS TOPICS Bayesian Methods in Meta-analysis Meta Regression Meta-analysis of Different Types of Data Incorporating Study Quality into a Meta-analysis Meta-analysis of Multiple and Correlated Outcome Measures Meta-analysis of Epidemiological and other Observational Studies Generalised Synthesis of Evidence - Combining Different Sources of Evidence Meta-analysis of Survival Data Cumulative Meta-analysis Miscellaneous and Developing Areas of Applications in Meta-Analysis Appendix I: Software Used for the Examples in this Book

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Book SynopsisQueueing Systems Volume 1: Theory Leonard Kleinrock This book presents and develops methods from queueing theory in sufficient depth so that students and professionals may apply these methods to many modern engineering problems, as well as conduct creative research in the field.Table of ContentsA Queueing Theory Primer. Bounds. Inequalities and Approximations. Priority Queueing. Computer Time-Sharing and Multiaccess Systems. Computer-Communication Networks: Analysis and Design. Computer-Communication Networks: Measurement, Flow Control, and ARPANET Traps.

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Book SynopsisThis work covers stochastic order relations, which provide insight into the behaviour of complex stochastic (random) systems and enables the user to collect comparative data. Application areas include queuing systems, actuarial and financial risk, decision making, and stochastic simulation.Trade Review"…a noteworthy contribution to applied probability, and I would recommend it to anyone interested in applied stochastic modeling." (Journal of the American Statistical Association, June 2005) “…will replace the excellent but now slightly dated text by Shaked and Shathikumar (1994) as the standard reference on stochastic orders.” (Statistical Papers, Vol.46, No.1, January 2005) "...provides an up-to-date survey of a notable area..." (Mathematical Reviews, 2003d) "...discusses the major concepts related to stochastic orders..." (SciTech Book News, Vol. 26, No. 2, June 2002) "...a very timely and methodically orientated book..." (Zentralblatt Math, Vol.999, No.24, 2002)Table of ContentsPreface. Univariate Stochastic Orders Theory of Integral Stochastic Orders Multivariate Stochastic Orders Stochastic Models, Comparison and Monotonicity Monotonicity and Comparability of Stochastic Processes Monotonicity Properties and Bounds for Queueing Systems Applications to Various Stochastic Models Comparing Risks. List of Symbols. References. Index.

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Book SynopsisAll students and researchers in environmental and biological sciences require statistical methods at some stage of their work. Many have a preconception that statistics are difficult and unpleasant and find that the textbooks available are difficult to understand. Practical Statistics for Environmental and Biological Scientists provides a concise, user-friendly, non-technical introduction to statistics. The book covers planning and designing an experiment, how to analyse and present data, and the limitations and assumptions of each statistical method. The text does not refer to a specific computer package but descriptions of how to carry out the tests and interpret the results are based on the approaches used by most of the commonly used packages, e.g. Excel, MINITAB and SPSS. Formulae are kept to a minimum and relevant examples are included throughout the text.Trade Review"The reassuring tone and straightforward approach of the book would be a useful guide...” (Biochemistry and Molecular Education, July/August 2002) "...covers the basics of designing an experiment/survey, data analysis and presentation, and specific methods." (SciTech Book News, Vol. 26, No. 2, June 2002) "...a good and clear exposition of basic statistical techniques..." (Biometrics, December 2002) "…This no-nonsense approach to elementary statistics should get you or your student started…" (European Journal of Soil Science, March 2003) "...This book provides a concise, userfriendly, non-technical introduction to statistics". (Metrohm Information, Vol.32, No.1, 2003)Table of ContentsPreface ix Part I Statistics Basics 1 1 Introduction 3 1.1 Do you need statistics? 3 1.2 What is statistics? 4 1.3 Some important lessons I have learnt 5 1.4 Statistics is getting easier 6 1.5 Integrity in statistics 7 1.6 About this book 8 2 A Brief Tutorial on Statistics 9 2.1 Introduction 9 2.2 Variability 9 2.3 Samples and populations 10 2.4 Summary statistics 11 2.5 The basis of statistical tests 19 2.6 Limitations of statistical tests 24 3 Before You Start 27 3.1 Introduction 27 3.2 What statistical methods are available? 28 3.3 Surveys and experiments 33 3.4 Designing experiments and surveys — preliminaries 35 3.5 Summary 43 4 Designing an Experiment or Survey 45 4.1 Introduction 45 4.2 Sample size 45 4.3 Sampling 50 4.4 Experimental design 56 4.5 Further reading 60 5 Exploratory Data Analysis and Data Presentation 63 5.1 Introduction 63 5.2 Column graphs 65 5.3 Line graphs 67 5.4 Scatter graphs 69 5.5 General points about graphs 71 5.6 Tables 73 5.7 Standard errors and error bars 74 6 Common Assumptions or Requirements of Data for Statistical Tests 77 6.1 Introduction 77 6.2 Common assumptions 81 6.3 Transforming data 84 Part II Statistical Methods 91 7 t-tests and F-tests 93 7.1 Introduction 93 7.2 Limitations and assumptions 94 7.3 t-tests 95 7.4 F-test 103 7.5 Further reading 105 8 Analysis of Variance 107 8.1 Introduction 107 8.2 Limitations and assumptions 109 8.3 One-way ANOVA 111 8.4 Multiway ANOVA 119 8.5 Further reading 127 9 Correlation and Regression 129 9.1 Introduction 129 9.2 Limitations and assumptions 130 9.3 Pearson’s product moment correlation 131 9.4 Simple linear regression 135 9.5 Correlation or regression? 142 9.6 Multiple linear regression 143 9.7 Comparing two lines 146 9.8 Fitting curves 148 9.9 Further reading 151 10 Multivariate ANOVA 153 10.1 Introduction 153 10.2 Limitations and assumptions 154 10.3 Null hypothesis 156 10.4 Description of the test 156 10.5 Interpreting the results 158 10.6 Further reading 161 11 Repeated Measures 163 11.1 Introduction 163 11.2 Methods for analysing repeated measures data 166 11.3 Designing repeated measures experiments 170 11.4 Further reading 170 12 Chi-square Tests 173 12.1 Introduction 173 12.2 Limitations and assumptions 174 12.3 Goodness of fit test 175 12.4 Test for association between two factors 178 12.5 Comparing proportions 181 12.6 Further reading 184 13 Non-parametric Tests 185 13.1 Introduction 185 13.2 Limitations and assumptions 188 13.3 Mann—Whitney U-test 189 13.4 Two-sample Kolmogorov—Smirnov test 191 13.5 Two-sample sign test 193 13.6 Kruskal—Wallis test 195 13.7 Friedman’s test 198 13.8 Spearman’s rank correlation 200 13.9 Further reading 203 14 Principal Component Analysis 205 14.1 Introduction 205 14.2 Limitations and assumptions 207 14.3 Description of the method 207 14.4 Interpreting the results 209 14.5 Further reading 218 15 Cluster Analysis 221 15.1 Introduction 221 15.2 Limitations and assumptions 222 15.3 Clustering observations 223 15.4 Clustering variables 226 15.5 Further reading 228 Appendices 229 A Calculations for statistical tests 231 B Concentration data for Chapters 14 and 15 247 C Using computer packages 249 D Choosing a test: decision table 261 E List of worked examples 265 Bibliography 271 Index 273

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Book SynopsisThe author presents a well tested approach using real examples taken from bio-medical research. He breaks down each problem into its components and where an unbiased partial test is found to exist, nonparametric combination methodology is used to determine overall solutions.Trade Review"the book is well written. It cand be useful and recommended for researchers and practitioners in a number of scientific disciplines...and for graduate students..." (Zentralblatt MATH, Vol.972, No.12, 2001) "...carefully presents a concise and mathematically rigorous treatment of permutation testing...could be used for a mathematically oriented graduate class...will form a source of recent reference material for research workers..." (Short Book Reviews, Vol. 22, No. 1, April 2002) "This book may herald a new era in biostatistics..." (Psychotherpay and Psychosomatics, September/October 2002) "...graduate and post-graduate students in some areas of physics and chemistry can benefit greatly from reading and using this book..." (The Statistician, Date Unknown)Table of ContentsPreface. Notation and Abbreviations. Introduction. Discussion of a Simple Testing Problem. Theory of Permutation Tests for One-Sample Problems. Examples of Univariate Multi-Sample Problems. Theory of Permutation Tests for Multi-Sample Problems. Nonparametric Combination Methodology. Examples of Nonparametric Combination. Permutation Analysis in Factorial Designs. Permutation Testing with Missing Data. The Behrens--Fisher Permutation Problem. Permutation Testing for Repeated Measurements. Further Applications. References. Index.

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Book SynopsisA guide which uses a problem solving approach and shows how to implement Monte Carlo methods, starting from first principles to advanced techniques.Table of ContentsPreface xi Acknowledgements xiii Mathematical Notation xv 1 Introduction 1 2 The Mathematics Behind Monte Carlo Methods 5 2.1 A Few Basic Terms in Probability and Statistics 5 2.2 Monte Carlo Simulations 7 2.2.1 Monte Carlo Supremacy 8 2.2.2 Multi-dimensional Integration 8 2.3 Some Common Distributions 9 2.4 Kolmogorov’s Strong Law 18 2.5 The Central Limit Theorem 18 2.6 The Continuous Mapping Theorem 19 2.7 Error Estimation for Monte Carlo Methods 20 2.8 The Feynman–Kac Theorem 21 2.9 The Moore–Penrose Pseudo-inverse 21 3 Stochastic Dynamics 23 3.1 Brownian Motion 23 3.2 Itô’s Lemma 24 3.3 Normal Processes 25 3.4 Lognormal Processes 26 3.5 The Markovian Wiener Process Embedding Dimension 26 3.6 Bessel Processes 27 3.7 Constant Elasticity Of Variance Processes 28 3.8 Displaced Diffusion 29 4 Process-driven Sampling 31 4.1 Strong versus Weak Convergence 31 4.2 Numerical Solutions 32 4.2.1 The Euler Scheme 32 4.2.2 The Milstein Scheme 33 4.2.3 Transformations 33 4.2.4 Predictor–Corrector 35 4.3 Spurious Paths 36 4.4 Strong Convergence for Euler and Milstein 37 5 Correlation and Co-movement 41 5.1 Measures for Co-dependence 42 5.2 Copulæ 45 5.2.1 The Gaussian Copula 46 5.2.2 The t-Copula 49 5.2.3 Archimedean Copulae 51 6 Salvaging a Linear Correlation Matrix 59 6.1 Hypersphere Decomposition 60 6.2 Spectral Decomposition 61 6.3 Angular Decomposition of Lower Triangular Form 62 6.4 Examples 63 6.5 Angular Coordinates on a Hypersphere of Unit Radius 65 7 Pseudo-random Numbers 67 7.1 Chaos 68 7.2 The Mid-square Method 72 7.3 Congruential Generation 72 7.4 Ran0 To Ran3 74 7.5 The Mersenne Twister 74 7.6 Which One to Use? 75 8 Low-discrepancy Numbers 77 8.1 Discrepancy 78 8.2 Halton Numbers 79 8.3 Sobol’ Numbers 80 8.3.1 Primitive Polynomials Modulo Two 81 8.3.2 The Construction of Sobol’ Numbers 82 8.3.3 The Gray Code 83 8.3.4 The Initialisation of Sobol’ Numbers 85 8.4 Niederreiter (1988) Numbers 88 8.5 Pairwise Projections 88 8.6 Empirical Discrepancies 91 8.7 The Number of Iterations 96 8.8 Appendix 96 8.8.1 Explicit Formula for the L2-norm Discrepancy on the Unit Hypercube 96 8.8.2 Expected L2-norm Discrepancy of Truly Random Numbers 97 9 Non-uniform Variates 99 9.1 Inversion of the Cumulative Probability Function 99 9.2 Using a Sampler Density 101 9.2.1 Importance Sampling 103 9.2.2 Rejection Sampling 104 9.3 Normal Variates 105 9.3.1 The Box–Muller Method 105 9.3.2 The Neave Effect 106 9.4 Simulating Multivariate Copula Draws 109 10 Variance Reduction Techniques 111 10.1 Antithetic Sampling 111 10.2 Variate Recycling 112 10.3 Control Variates 113 10.4 Stratified Sampling 114 10.5 Importance Sampling 115 10.6 Moment Matching 116 10.7 Latin Hypercube Sampling 119 10.8 Path Construction 120 10.8.1 Incremental 120 10.8.2 Spectral 122 10.8.3 The Brownian Bridge 124 10.8.4 A Comparison of Path Construction Methods 128 10.8.5 Multivariate Path Construction 131 10.9 Appendix 134 10.9.1 Eigenvalues and Eigenvectors of a Discrete-time Covariance Matrix 134 10.9.2 The Conditional Distribution of the Brownian Bridge 137 11 Greeks 139 11.1 Importance Of Greeks 139 11.2 An Up-Out-Call Option 139 11.3 Finite Differencing with Path Recycling 140 11.4 Finite Differencing with Importance Sampling 143 11.5 Pathwise Differentiation 144 11.6 The Likelihood Ratio Method 145 11.7 Comparative Figures 147 11.8 Summary 153 11.9 Appendix 153 11.9.1 The Likelihood Ratio Formula for Vega 153 11.9.2 The Likelihood Ratio Formula for Rho 156 12 Monte Carlo in the BGM/J Framework 159 12.1 The Brace–Gatarek–Musiela/Jamshidian Market Model 159 12.2 Factorisation 161 12.3 Bermudan Swaptions 163 12.4 Calibration to European Swaptions 163 12.5 The Predictor–Corrector Scheme 169 12.6 Heuristics of the Exercise Boundary 171 12.7 Exercise Boundary Parametrisation 174 12.8 The Algorithm 176 12.9 Numerical Results 177 12.10 Summary 182 13 Non-recombining Trees 183 13.1 Introduction 183 13.2 Evolving the Forward Rates 184 13.3 Optimal Simplex Alignment 187 13.4 Implementation 190 13.5 Convergence Performance 191 13.6 Variance Matching 192 13.7 Exact Martingale Conditioning 195 13.8 Clustering 196 13.9 A Simple Example 199 13.10 Summary 200 14 Miscellanea 201 14.1 Interpolation of the Term Structure of Implied Volatility 201 14.2 Watch Your CPU Usage 202 14.3 Numerical Overflow and Underflow 205 14.4 A Single Number or a Convergence Diagram? 205 14.5 Embedded Path Creation 206 14.6 How Slow is Exp()? 207 14.7 Parallel Computing And Multi-threading 209 Bibliography 213 Index 219

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Book SynopsisREAD ALL ABOUT IT! David Spiegelhalter has recently joined the ranks of Isaac Newton, Charles Darwin and Stephen Hawking by becoming a fellow of the Royal Society.Originating from the Medical Research Council's biostatistics unit, David has played a leading role in the Bristol heart surgery and Harold Shipman inquiries. Order a copy of this author's comprehensive text TODAY! The Bayesian approach involves synthesising data and judgement in order to reach conclusions about unknown quantities and make predictions. Bayesian methods have become increasingly popular in recent years, notably in medical research, and although there are a number of books on Bayesian analysis, few cover clinical trials and biostatistical applications in any detail. Bayesian Approaches to Clinical Trials and Health-Care Evaluation provides a valuable overview of this rapidly evolving field, including basic Bayesian ideas, prior distributions, clinical trials, observational studies, evidence synTrade Review"This is a terrific book and should be on the shelf of every professional that works in clinical trials or health-care evaluation. It gives a thorough pragmatic introduction to Bayesian methods for health-care interventions, provides many example along with data and software to reproduce the analyses, guides readers to areas where Bayesian methods are particularly valuable, and includes an excellent set of exercises." (Journal of the American Statistical Association, June 2009) "Bayesian Approaches to Clinical Trials and Health-Care Evaluation' is a clear and comprehensive text for biostatisticians who want to understand and apply Bayesian statistical methods to clinical research." (Journal of Clinical Best Practices, Nov 2008) "…an indispensable resource for all students and investigators who plan to incorporate Bayesian methods into their research." (The Annals of Pharmacotherapy, January 2005) "...a valuable resource for libraries, and those who are involved in quantitative health care evaluation..." (Royal Statistical Society, Vol.168, No.1, January 2005) "...The technical material is presented in an accessible style, and the examples given clearly illustrate the principles under discussion..." (Short Book Reviews, Vol.24, No.3, December 2004) "...Bayesian analysis seems set to reach a wider audience with the publication of [this] introductory level text..." (Financial Times, 16 April 2004) "...very well laid-out and easy to follow...a very good resource for teaching students..." (Statistical Methods in Medical Research, Vol 14, 2005) "I would use with pleasure and interest this book as a textbook..." (Metron Journal, Vol.63, No.2, 2005) "...I can pay the authors no higher tribute than to say that I would be proud to have written this book. It is elegant and it is destined to becoming a classic in the field." (Statistics in Medicine, 15th July 2005) "...a generous supply of exercises...I recommend it very highly..." (Clinical Trials, No.1 2004) "...Bayesian analysis seems set to reach a wider audience with the publication of [this] introductory level text..." (Financial Times, 16 April 2004) "...a generous supply of exercises...I recommend it very highly..." (Clinical Trials, No.1 2004)Table of ContentsPreface. List of examples. 1. Introduction. 1.1 What are Bayesian methods? 1.2 What do we mean by ‘health-care evaluation’? 1.3 A Bayesian approach to evaluation. 1.4 The aim of this book and the intended audience. 1.5 Structure of the book. 2. Basic Concepts from Traditional Statistical Analysis. 2.1 Probability. 2.1.1 What is probability? 2.1.2 Odds and log-odds. 2.1.3 Bayes theorem for simple events. 2.2 Random variables, parameters and likelihood. 2.2.1 Random variables and their distributions. 2.2.2 Expectation, variance, covariance and correlation. 2.2.3 Parametric distributions and conditional independence. 2.2.4 Likelihoods. 2.3 The normal distribution. 2.4 Normal likelihoods. 2.4.1 Normal approximations for binary data. 2.4.2 Normal likelihoods for survival data. 2.4.3 Normal likelihoods for count responses. 2.4.4 Normal likelihoods for continuous responses. 2.5 Classical inference. 2.6 A catalogue of useful distributions*. 2.6.1 Binomial and Bernoulli. 2.6.2 Poisson. 2.6.3 Beta. 2.6.4 Uniform. 2.6.5 Gamma. 2.6.6 Root-inverse-gamma. 2.6.7 Half-normal. 2.6.8 Log-normal. 2.6.9 Student’s t. 2.6.10 Bivariate normal. 2.7 Key points. Exercises. 3. An Overview of the Bayesian Approach. 3.1 Subjectivity and context. 3.2 Bayes theorem for two hypotheses. 3.3 Comparing simple hypotheses: likelihood ratios and Bayes factors. 3.4 Exchangeability and parametric modelling*. 3.5 Bayes theorem for general quantities. 3.6 Bayesian analysis with binary data. 3.6.1 Binary data with a discrete prior distribution. 3.6.2 Conjugate analysis for binary data. 3.7 Bayesian analysis with normal distributions. 3.8 Point estimation, interval estimation and interval hypotheses. 3.9 The prior distribution. 3.10 How to use Bayes theorem to interpret trial results. 3.11 The ‘credibility’ of significant trial results*. 3.12 Sequential use of Bayes theorem*. 3.13 Predictions. 3.13.1 Predictions in the Bayesian framework. 3.13.2 Predictions for binary data*. 3.13.3 Predictions for normal data. 3.14 Decision-making. 3.15 Design. 3.16 Use of historical data. 3.17 Multiplicity, exchangeability and hierarchical models. 3.18 Dealing with nuisance parameters*. 3.18.1 Alternative methods for eliminating nuisance parameters*. 3.18.2 Profile likelihood in a hierarchical model*. 3.19 Computational issues. 3.19.1 Monte Carlo methods. 3.19.2 Markov chain Monte Carlo methods. 3.19.3 WinBUGS. 3.20 Schools of Bayesians. 3.21 A Bayesian checklist. 3.22 Further reading. 3.23 Key points. Exercises. 4. Comparison of Alternative Approaches to Inference. 4.1 A structure for alternative approaches. 4.2 Conventional statistical methods used in health-care evaluation. 4.3 The likelihood principle, sequential analysis and types of error. 4.3.1 The likelihood principle. 4.3.2 Sequential analysis. 4.3.3 Type I and Type II error. 4.4 P-values and Bayes factors*. 4.4.1 Criticism of P-values. 4.4.2 Bayes factors as an alternative to P-values: simple hypotheses. 4.4.3 Bayes factors as an alternative to P-values: composite hypotheses. 4.4.4 Bayes factors in preference studies. 4.4.5 Lindley’s paradox. 4.5 Key points. Exercises. 5. Prior Distributions. 5.1 Introduction. 5.2 Elicitation of opinion: a brief review. 5.2.1 Background to elicitation. 5.2.2 Elicitation techniques. 5.2.3 Elicitation from multiple experts. 5.3 Critique of prior elicitation. 5.4 Summary of external evidence*. 5.5 Default priors. 5.5.1 ‘Non-informative’ or ‘reference’ priors: 5.5.2 ‘Sceptical’ priors. 5.5.3 ‘Enthusiastic’ priors. 5.5.4 Priors with a point mass at the null hypothesis (‘lump-and-smear’ priors)*. 5.6 Sensitivity analysis and ‘robust’ priors. 5.7 Hierarchical priors. 5.7.1 The judgement of exchangeability. 5.7.2 The form for the random-effects distribution. 5.7.3 The prior for the standard deviation of the random effects*. 5.8 Empirical criticism of priors. 5.9 Key points. Exercises. 6. Randomised Controlled Trials. 6.1 Introduction. 6.2 Use of a loss function: is a clinical trial for inference or decision? 6.3 Specification of null hypotheses. 6.4 Ethics and randomisation: a brief review. 6.4.1 Is randomisation necessary? 6.4.2 When is it ethical to randomise? 6.5 Sample size of non-sequential trials. 6.5.1 Alternative approaches to sample-size assessment. 6.5.2 ‘Classical power’: hybrid classical-Bayesian methods assuming normality. 6.5.3 ‘Bayesian power’. 6.5.4 Adjusting formulae for different hypotheses. 6.5.5 Predictive distribution of power and necessary sample size. 6.6 Monitoring of sequential trials. 6.6.1 Introduction. 6.6.2 Monitoring using the posterior distribution. 6.6.3 Monitoring using predictions: ‘interim power’. 6.6.4 Monitoring using a formal loss function. 6.6.5 Frequentist properties of sequential Bayesian methods. 6.6.6 Bayesian methods and data monitoring committees. 6.7 The role of ‘scepticism’ in confirmatory studies. 6.8 Multiplicity in randomised trials. 6.8.1 Subset analysis. 6.8.2 Multi-centre analysis. 6.8.3 Cluster randomization. 6.8.4 Multiple endpoints and treatments. 6.9 Using historical controls*. 6.10 Data-dependent allocation. 6.11 Trial designs other than two parallel groups. 6.12 Other aspects of drug development. 6.13 Further reading. 6.14 Key points. Exercises. 7. Observational Studies. 7.1 Introduction. 7.2 Alternative study designs. 7.3 Explicit modelling of biases. 7.4 Institutional comparisons. 7.5 Key points. Exercises. 8. Evidence Synthesis. 8.1 Introduction. 8.2 ‘Standard’ meta-analysis. 8.2.1 A Bayesian perspective. 8.2.2 Some delicate issues in Bayesian meta-analysis. 8.2.3 The relationship between treatment effect and underlying risk. 8.3 Indirect comparison studies. 8.4 Generalised evidence synthesis. 8.5 Further reading. 8.6 Key points. Exercises. 9. Cost-effectiveness, Policy-Making and Regulation. 9.1 Introduction. 9.2 Contexts. 9.3 ‘Standard’ cost-effectiveness analysis without uncertainty. 9.4 ‘Two-stage’ and integrated approaches to uncertainty in cost-effectiveness modeling. 9.5 Probabilistic analysis of sensitivity to uncertainty about parameters: two-stage approach. 9.6 Cost-effectiveness analyses of a single study: integrated approach. 9.7 Levels of uncertainty in cost-effectiveness models. 9.8 Complex cost-effectiveness models. 9.8.1 Discrete-time, discrete-state Markov models. 9.8.2 Micro-simulation in cost-effectiveness models. 9.8.3 Micro-simulation and probabilistic sensitivity analysis. 9.8.4 Comprehensive decision modeling. 9.9 Simultaneous evidence synthesis and complex cost-effectiveness modeling. 9.9.1 Generalised meta-analysis of evidence. 9.9.2 Comparison of integrated Bayesian and two-stage approach. 9.10 Cost-effectiveness of carrying out research: payback models. 9.10.1 Research planning in the public sector. 9.10.2 Research planning in the pharmaceutical industry. 9.10.3 Value of information. 9.11 Decision theory in cost-effectiveness analysis, regulation and policy. 9.12 Regulation and health policy. 9.12.1 The regulatory context. 9.12.2 Regulation of pharmaceuticals. 9.12.3 Regulation of medical devices. 9.13 Conclusions. 9.14 Key points. Exercises. 10. Conclusions and Implications for Future Research. 10.1 Introduction. 10.2 General advantages and problems of a Bayesian approach. 10.3 Future research and development. Appendix: Websites and Software. A.1 The site for this book. A.2 Bayesian methods in health-care evaluation. A.3 Bayesian software. A.4 General Bayesian sites. References. Index.

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Book SynopsisPresents methods for the design and analysis of surveys, studies, and experiments when the data is qualitative and categorical. This work also covers the delta methods for multinomial frequencies. It discusses topics in misclassification and in reliability assessment.Trade Review"A well written specialized book by Fleiss et al. illustrates in detail the definitions and importance of rates in health and other data analysis." (Journal of Statistical Computation and Simulation, April 2005) "…the definitive text of context, method and application for the efficient analysis of rates and proportions…" (Statistics in Medicine, Vol 24 (17), 15th September 2005) "…well written in a thoroughly readable style. I highly recommend this book…" (Statistical Methods in Medical Research, Vol. 14, 2005) "…persons who regularly encounter this type of data would certainly want this book available as one of their desk-top references." (Technometrics, May 2004)Table of ContentsPreface. Preface to the Second Edition. Preface to the First Edition. 1. An Introduction to Applied Probability. 2. Statistical Inference for a Single Proportion. 3. Assessing Significance in a Fourfold Table. 4. Determining Sample Sizes Needed to Detect a Difference Between Two Proportions. 5. How to Randomize. 6. Comparative Studies: Cross-Sectional, Naturalistic, or Multinomial Sampling. 7. Comparative Studies: Prospective and Retrospective Sampling. 8. Randomized Controlled Trials. 9. The Comparison of Proportions from Several Independent Samples. 10. Combining Evidence from Fourfold Tables. 11. Logistic Regression. 12. Poisson Regression. 13. Analysis of Data from Matched Samples. 14. Regression Models for Matched Samples. 15. Analysis of Correlated Binary Data. 16. Missing Data. 17. Misclassification Errors: Effects, Control, and Adjustment. 18. The Measurement of Interrater Agreement. 19. The Standardization of Rates. Appendix A. Numerical Tables. Appendix B. The Basic Theory of Maximum Likelihood Estimation. Appendix C. Answers to Selected Problems. Author Index. Subject Index.

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Book SynopsisThe subject of time series is of considerable interest, especiallyamong researchers in econometrics, engineering, and the naturalsciences. As part of the prestigious Wiley Series in Probabilityand Statistics, this book provides a lucid introduction to thefield and, in this new Second Edition, covers the importantadvances of recent years, including nonstationary models, nonlinearestimation, multivariate models, state space representations, andempirical model identification. New sections have also been addedon the Wold decomposition, partial autocorrelation, long memoryprocesses, and the Kalman filter. Major topics include: * Moving average and autoregressive processes * Introduction to Fourier analysis * Spectral theory and filtering * Large sample theory * Estimation of the mean and autocorrelations * Estimation of the spectrum * Parameter estimation * Regression, trend, and seasonality * Unit root and explosive time series To accomTable of ContentsMoving Average and Autoregressive Processes. Introduction to Fourier Analysis. Spectral Theory and Filtering. Some Large Sample Theory. Estimation of the Mean and Autocorrelations. The Periodogram, Estimated Spectrum. Parameter Estimation. Regression, Trend, and Seasonality. Unit Root and Explosive Time Series. Bibliography. Index.

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Book SynopsisDesigned to aid readers in gathering the most reliable quantitative information on forests for the least cost.Table of ContentsFocus, Fundamental Concepts, and Theory. Probabilistic Sampling Strategies. Forest Sampling--Single Level. Multi-Information Sources for Sampling. Model-Based Inference. Mensurational Aspects of Forest Inventory. Related Sampling Topics. Related Estimation Topics. Future Directions in Multiresource Sampling in Forestry. References. Answers to the Problems. Index.

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Book SynopsisQueueing theory is an effective tool for studying several performance parameters of computer systems. This book discusses the difficult subject of queuing theory is by working on information processing problems.Table of ContentsA Queueing Theory Primer. Random Processes. Birth-Death Queueing Systems. Markovian Queues. The Queue M/G/1. The Queue G/M/m. The Queue G/G/1. Index.

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Book SynopsisThis book discusses adaptive sampling designs which are used in surveys where data collection requires modification as a result of observations made during the process. The strategies detailed in the book offer solutions to the long-standing problem of estimating the abundance of rare, clustered populations.Table of ContentsFixed-Population Sampling Theory. Stochastic Population Sampling Theory. Adaptive Cluster Sampling. Efficiency and Sample Size Issues. Adaptive Cluster Sampling Based on Order Statistics. Adaptive Allocation in Stratified Sampling. Multivariate Aspects of Adaptive Sampling. Detectability in Adaptive Sampling. Optimal Sampling Strategies. References. Index.

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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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