Introduction to WinBUGS for ecologists : a Bayesian approach to regression, ANOVA, mixed models and related analyses

Bayesian statistics has exploded into biology and its sub-disciplines such as ecology over the past decade. The free software program WinBUGS and its open-source sister OpenBugs is currently the only flexible and general-purpose program available with which the average ecologist can conduct their own standard and non-standard Bayesian statistics. Introduction to WINBUGS for Ecologists goes right to the heart of the matter by providing ecologists with a comprehensive, yet concise, guide to applying WinBUGS to the types of models that they use most often: linear (LM), generalized linear (GLM), linear mixed (LMM) and generalized linear mixed models (GLMM). Introduction to WinBUGS for Ecologists combines the use of simulated data sets "paired" analyses using WinBUGS (in a Bayesian framework for analysis) and in R (in a frequentist mode of inference) and uses a very detailed step-by-step tutorial presentation style that really lets the reader repeat every step of the application of a given mode in their own research. - 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 - Written with ecological language and ecological examples - Companion Web Appendix that contains all code contained in the book, additional material (including more code and solutions to exercises) - Tutorial approach shows ecologists how to implement Bayesian analysis in practical problems that they face Introduction to WinBUGS for Ecologists: A Bayesian Approach to Regression, Anova, Mixed Models, and Related Analyses......Page 1 Copyright......Page 2 A Creed for Modeling......Page 3 Foreword......Page 4 Preface......Page 8 Acknowledgments......Page 11 Introduction......Page 12 Ease of Error Propagation......Page 13 Intuitive Appeal......Page 14 WinBUGS......Page 15 Why This Book?......Page 16 Juxtaposition of Classical and Bayesian Analyses......Page 17 The Power of Simulating Data......Page 18 What This Book Is Not About: Theory of Bayesian Statistics and Computation......Page 19 Further Reading......Page 20 Summary......Page 22 Introduction to the Bayesian Analysis of a Statistical Model......Page 23 Probability Theory and Statistics......Page 24 Two Views of Statistics: Classical and Bayesian......Page 25 Markov chain Monte Carlo (MCMC) and Gibbs Sampling......Page 29 Convergence Monitoring......Page 31 Computing Functions of Parameters......Page 33 Hypothesis Tests and Model Selection......Page 34 Parameter Identifiability......Page 36 Summary......Page 37 What Is WinBUGS?......Page 39 WinBUGS Frees the Modeler in You......Page 40 Some Technicalities and Conventions......Page 41 Introduction......Page 43 Setting Up the Analysis......Page 44 Starting the MCMC Blackbox......Page 50 Summarizing the Results......Page 51 Summary......Page 54 Introduction......Page 56 Data Generation......Page 57 Analysis Using WinBUGS......Page 58 Summary......Page 64 Key Components of (Generalized) Linear Models: Statistical Distributions and the Linear Predictor......Page 66 Introduction......Page 67 Stochastic Part of Linear Models: Statistical Distributions......Page 68 Normal Distribution......Page 70 Binomial Distribution: The “Coin-Flip Distribution”......Page 71 Poisson Distribution......Page 74 Deterministic Part of Linear Models: Linear Predictor and Design Matrices......Page 75 The Model of the Mean......Page 77 t-Test......Page 78 Simple Linear Regression......Page 82 One-Way Analysis of Variance......Page 85 Two-Way Analysis of Variance......Page 87 Analysis of Covariance......Page 91 Summary......Page 98 t-Test: Equal and Unequal Variances......Page 99 Data Generation......Page 100 Analysis Using R......Page 101 Analysis Using WinBUGS......Page 102 Data Generation......Page 105 Analysis Using R......Page 106 Analysis Using WinBUGS......Page 107 Summary and a Comment on the Modeling of Variances......Page 108 Introduction......Page 110 Data Generation......Page 111 Fitting the Model......Page 112 Goodness-of-Fit Assessment in Bayesian Analyses......Page 113 Forming Predictions......Page 116 Interpretation of Confidence vs. Credible Intervals......Page 118 Summary......Page 120 Introduction: Fixed and Random Effects......Page 121 Data Generation......Page 125 Bayesian Analysis Using WinBUGS......Page 126 Data Generation......Page 128 Restricted Maximum Likelihood Analysis Using R......Page 130 Bayesian Analysis Using WinBUGS......Page 131 Summary......Page 133 Introduction: Main and Interaction Effects......Page 134 Data Generation......Page 136 Aside: Using Simulation to Assess Bias and Precision of an Estimator......Page 138 Analysis Using R......Page 139 Main-Effects ANOVA Using WinBUGS......Page 140 Interaction-Effects ANOVA Using WinBUGS......Page 142 Forming Predictions......Page 143 Summary......Page 144 Introduction......Page 145 Data Generation......Page 147 Analysis Using WinBUGS (and a Cautionary Tale About the Importance of Covariate Standardization)......Page 149 Summary......Page 153 Introduction......Page 155 Data Generation......Page 158 Bayesian Analysis Using WinBUGS......Page 160 REML Analysis Using R......Page 162 Bayesian Analysis Using WinBUGS......Page 163 Introduction......Page 165 Data Generation......Page 166 REML Analysis Using R......Page 167 Bayesian Analysis Using WinBUGS......Page 168 Summary......Page 169 Introduction......Page 171 Data Generation......Page 174 Analysis Using WinBUGS......Page 175 Check of Markov Chain Monte Carlo Convergence and Model Adequacy......Page 177 Inference Under the Model......Page 178 Summary......Page 181 Overdispersion, Zero-Inflation, and Offsets in the GLM......Page 182 Data Generation......Page 183 Analysis Using R......Page 184 Analysis Using WinBUGS......Page 186 Introduction......Page 187 Data Generation......Page 188 Analysis Using R......Page 189 Analysis Using WinBUGS......Page 190 Introduction......Page 191 Analysis Using WinBUGS......Page 192 Summary......Page 193 Introduction......Page 195 Data Generation......Page 196 Analysis Using R......Page 198 Fitting the Model......Page 199 Forming Predictions......Page 201 Summary......Page 203 Introduction......Page 205 Data Generation......Page 207 Analysis Under a Random-Coefficients Model......Page 208 Analysis Using WinBUGS......Page 209 Summary......Page 211 Introduction......Page 212 Analysis Using R......Page 214 Analysis Using WinBUGS......Page 215 Summary......Page 217 Introduction......Page 219 Data Generation......Page 221 Analysis Using R......Page 223 Analysis Using WinBUGS......Page 224 Summary......Page 228 Introduction......Page 229 Data Generation......Page 230 Analysis Under a Random-Coefficients Model......Page 231 Analysis Using R......Page 232 Analysis Using WinBUGS......Page 234 Summary......Page 236 Introduction......Page 237 Data Generation......Page 242 Analysis Using WinBUGS......Page 246 Summary......Page 251 Introduction......Page 253 Data Generation......Page 257 Analysis Using WinBUGS......Page 262 Summary......Page 273 Conclusions......Page 275 A List of WinBUGS Tricks......Page 278 References......Page 284 B......Page 289 C......Page 290 D......Page 291 F......Page 292 I......Page 293 M......Page 294 O......Page 295 P......Page 296 R......Page 297 S......Page 298 W......Page 299 Z......Page 300

Bayesian statistics has exploded into biology and its sub-disciplines, such as ecology, over the past decade. The free software program WinBUGS and its open-source sister OpenBugs is currently the only flexible and general-purpose program available with which the average ecologist can conduct standard and non-standard Bayesian statistics. Introduction to WINBUGS for Ecologists goes right to the heart of the matter by providing ecologists with a comprehensive, yet concise, guide to applying WinBUGS to the types of models that they use most often: linear (LM), generalized linear (GLM), linear mixed (LMM) and generalized linear mixed models (GLMM).

Introduction to WinBUGS for Ecologists combines the use of simulated data sets "paired" analyses using WinBUGS (in a Bayesian framework for analysis) and in R (in a frequentist mode of inference) and uses a very detailed step-by-step tutorial presentation style that really lets the reader repeat every step of the application of a given mode in their own research.

• 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)

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 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 Introduction to Bayesian analysis of a statistical model WinBUGS A first session in WinBUGS : the "model of the mean" Running WinBUGS from R via R2WinBUGS Key components of (generalized) linear models : statistical distributions and the linear predictor t-Test : equal and unequal variances Normal linear regression Normal one-way ANOVA Normal two-way ANOVA General linear model (ANCOVA) Linear mixed-effects model Introduction to the generalized linear model : Poisson "t-test" Overdispersion, zero-inflation, and offsets in the GLM Poisson ANCOVA Poisson mixed-effects model (Poisson GLMM) Binomial "t-Test" Binomial analysis of covariance Binomial mixed-effects model (binomial GLMM) Nonstandard GLMMs 1 : site-occupancy species distribution model Nonstandard GLMMs 2 : binomial mixture model to model abundance Conclusions. Introduction to WinBUGS for Ecologists is an introduction to Bayesian statistical modeling, written for ecologists by an ecologist, using the widely available and free WinBUGS package. Examples are placed within a comprehensive and largely non-mathematical overview of linear, generalized linear (GLM), linear mixed and generalized linear mixed models (GLMM). This book will be interest to any quantitative scientist who uses regression-type models, especially ecologists, agronomists, geologists, epidemiologists, sociologists, and psychologists. --Book Jacket