Introduction to WinBUGS for Ecologists (eBook)

Bayesian Approach to Regression, ANOVA, Mixed Models and Related Analyses

Marc Kery (Autor)

eBook Download: EPUB

2010 | 1. Auflage
320 Seiten
Elsevier Science (Verlag)
978-0-12-378606-7 (ISBN)

Infos

Introduction to WinBUGS for Ecologists introduces applied Bayesian modeling to ecologists using the highly acclaimed, free WinBUGS software. It offers an understanding of statistical models as abstract representations of the various processes that give rise to a data set. Such an understanding is basic to the development of inference models tailored to specific sampling and ecological scenarios. The book begins by presenting the advantages of a Bayesian approach to statistics and introducing the WinBUGS software. It reviews the four most common statistical distributions: the normal, the uniform, the binomial, and the Poisson. It describes the two different kinds of analysis of variance (ANOVA): one-way and two- or multiway. It looks at the general linear model, or ANCOVA, in R and WinBUGS. It introduces generalized linear model (GLM), i.e., the extension of the normal linear model to allow error distributions other than the normal. The GLM is then extended contain additional sources of random variation to become a generalized linear mixed model (GLMM) for a Poisson example and for a binomial example. The final two chapters showcase two fairly novel and nonstandard versions of a GLMM. The first is the site-occupancy model for species distributions; the second is the binomial (or N-) mixture model for estimation and modeling of abundance.

• Introduction to the essential theories of key models used by ecologists
• Complete juxtaposition of classical analyses in R and Bayesian analysis of the same models in WinBUGS
• Provides every detail of R and WinBUGS code required to conduct all analyses
• Companion Web Appendix that contains all code contained in the book and additional material (including more code and solutions to exercises)

Dr Kery is a Population Ecologist with the Swiss Ornithological Institute and a courtesy professor ('Privatdozent') at the University of Zürich/Switzerland, from where he received his PhD in Ecology in 2000. He is an expert in the estimation and modeling of abundance, distribution and species richness in 'metapopulation designs' (i.e., collections of replicate sites). For most of his work, he uses the Bayesian model fitting software BUGS and JAGS, about which he has published two books with Academic Press (2010 and 2012). He has authored/coauthored 70 peer-reviewed articles and four book chapters. Since 2007, and for a total of 103 days, he has taught 23 statistical modeling workshops about the methods in the proposed book at research institutes and universities all over the world.

Inhalt

Front Cover 1
Introduction to WinBUGS for Ecologists 4
Copyright 5
A Creed for Modeling 6
Table of Contents 8
Foreword 12
Preface 16
Acknowledgments 19
Chapter 1. Introduction 20
1.1 Advantages of the Bayesian Approach to Statistics 21
1.2 So Why Then Isn’t Everyone a Bayesian? 23
1.3 WinBUGS 23
1.4 Why This Book? 24
1.5 What This Book Is Not About: Theory of Bayesian Statistics and Computation 27
1.6 Further Reading 28
1.7 Summary 30
Chapter 2. Introduction to the Bayesian Analysis of a Statistical Model 32
2.1 Probability Theory and Statistics 33
2.2 Two Views of Statistics: Classical and Bayesian 34
2.3 The Importance of Modern Algorithms and Computers for Bayesian Statistics 38
2.4 Markov chain Monte Carlo (MCMC) and Gibbs Sampling 38
2.5 What Comes after MCMC? 40
2.6 Some Shared Challenges in the Bayesian and the Classical Analysis of a Statistical Model 43
2.7 Pointer to Special Topics in This Book 46
2.8 Summary 46
Chapter 3. WinBUGS 48
3.1 What Is WinBUGS? 48
3.2 Running WinBUGS from R 49
3.3 WinBUGS Frees the Modeler in You 49
3.4 Some Technicalities and Conventions 50
Chapter 4. A First Session in WinBUGS: The “Model of the Mean” 52
4.1 Introduction 52
4.2 Setting Up the Analysis 53
4.3 Starting the MCMC Blackbox 59
4.4 Summarizing the Results 60
4.5 Summary 63
Chapter 5. Running WinBUGS from R via R2WinBUGS 66
5.1 Introduction 66
5.2 Data Generation 67
5.3 Analysis Using R 68
5.4 Analysis Using WinBUGS 68
5.5 Summary 74
Chapter 6. Key Components of (Generalized) Linear Models: Statistical Distributions and the Linear Predictor 76
6.1 Introduction 77
6.2 Stochastic Part of Linear Models: Statistical Distributions 78
6.3 Deterministic Part of Linear Models: Linear Predictor and Design Matrices 85
6.4 Summary 108
Chapter 7. t-Test: Equal and Unequal Variances 110
7.1 t-Test with Equal Variances 111
7.2 t-Test with Unequal Variances 116
7.3 Summary and a Comment on the Modeling of Variances 119
Chapter 8. Normal Linear Regression 122
8.1 Introduction 122
8.2 Data Generation 123
8.3 Analysis Using R 124
8.4 Analysis Using WinBUGS 124
8.5 Summary 132
Chapter 9. Normal One-Way ANOVA 134
9.1 Introduction: Fixed and Random Effects 134
9.2 Fixed-Effects ANOVA 138
9.3 Random-Effects ANOVA 141
9.4 Summary 146
Chapter 10. Normal Two-Way ANOVA 148
10.1 Introduction: Main and Interaction Effects 148
10.2 Data Generation 150
10.3 Aside: Using Simulation to Assess Bias and Precision of an Estimator 152
10.4 Analysis Using R 153
10.5 Analysis Using WinBUGS 154
10.6 Summary 158
Chapter 11. General Linear Model (ANCOVA) 160
11.1 Introduction 160
11.2 Data Generation 162
11.3 Analysis Using R 164
11.4 Analysis Using WinBUGS (And A Cautionary Tale About the Importance of Covariate Standardization) 164
11.5 Summary 168
Chapter 12. Linear Mixed-Effects Model 170
12.1 Introduction 170
12.2 Data Generation 173
12.3 Analysis under a Random-Intercepts Model 175
12.4 Analysis under a Random-Coefficients Model without Correlation between Intercept and Slope 177
12.5 The Random-Coefficients Model with Correlation between Intercept and Slope 180
12.6 Summary 184
Chapter 13. Introduction to the Generalized Linear Model: Poisson “t-test” 186
13.1 Introduction 186
13.2 An Important but Often Forgotten Issue with Count Data 189
13.3 Data Generation 189
13.4 Analysis Using R 190
13.5 Analysis Using WinBUGS 190
13.6 Summary 196
Chapter 14. Overdispersion, Zero-Inflation, and Offsets in the GLM 198
14.1 Overdispersion 199
14.2 Zero-Inflation 203
14.3 Offsets 207
14.4 Summary 209
Chapter 15. Poisson ANCOVA 212
15.1 Introduction 212
15.2 Data Generation 213
15.3 Analysis Using R 215
15.4 Analysis Using WinBUGS 216
15.5 Summary 220
Chapter 16. Poisson Mixed-Effects Model (Poisson GLMM) 222
16.1 Introduction 222
16.2 Data Generation 224
16.3 Analysis Under a Random-Coefficients Model 225
16.4 Summary 228
Chapter 17. Binomial “t-Test” 230
17.1 Introduction 230
17.2 Data Generation 232
17.3 Analysis Using R 232
17.4 Analysis Using WinBUGS 233
17.5 Summary 235
Chapter 18. Binomial Analysis of Covariance 238
18.1 Introduction 238
18.2 Data Generation 240
18.3 Analysis Using R 242
18.4 Analysis Using WinBUGS 243
18.5 Summary 247
Chapter 19. Binomial Mixed-Effects Model (Binomial GLMM) 248
19.1 Introduction 248
19.2 Data Generation 249
19.3 Analysis Under a Random-Coefficients Model 250
19.4 Summary 255
Chapter 20. Nonstandard GLMMs 1: Site-Occupancy Species Distribution Model 256
20.1 Introduction 256
20.2 Data Generation 261
20.3 Analysis Using WinBUGS 265
20.4 Summary 270
Chapter 21. Nonstandard GLMMs 2: Binomial Mixture Model to Model Abundance 272
21.1 Introduction 272
21.2 Data Generation 276
21.3 Analysis Using WinBUGS 281
21.4 Summary 292
Chapter 22. Conclusions 294
Appendix: A List of WinBUGS Tricks 298
References 304
Index 310

Produkt-Details

• Erscheint lt. Verlag: 19.7.2010
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Biologie ► Ökologie / Naturschutz
• Themenwelt: Technik ► Umwelttechnik / Biotechnologie
• ISBN-10: 0-12-378606-1 / 0123786061
• ISBN-13: 978-0-12-378606-7 / 9780123786067