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

✍ Scribed by Marc Kery

• Year: 2010
• Tongue: English
• Leaves: 300
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

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