Bayesian models: a statistical primer for ecologists

✍ Scribed by Hobbs, N Thompson;Hooten, Mevin B

• Publisher: Princeton University Press
• Year: 2015;2017
• Tongue: English
• Leaves: 315
• Category: Library

✦ Synopsis

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods--in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.

Bayesian Modelsis an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.

This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.



Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticians
Covers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and more
Deemphasizes computer coding in favor of basic principles
Explains how to write out properly factored statistical expressions representing Bayesian models

✦ Table of Contents

Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 10
I Fundamentals......Page 16
1 PREVIEW......Page 18
1.1 A Line of Inference for Ecology......Page 19
1.2 An Example Hierarchical Model......Page 26
1.3 What Lies Ahead?......Page 30
2.1 Modeling Styles in Ecology......Page 32
2.2 A Few Good Functions......Page 36
3.1 Why Bother with First Principles?......Page 44
3.2 Rules of Probability......Page 46
3.3 Factoring Joint Probabilities......Page 51
3.4 Probability Distributions......Page 54
4.1 Likelihood Functions......Page 86
4.2 Likelihood Profiles......Page 89
4.3 Maximum Likelihood......Page 91
4.4 The Use of Prior Information in Maximum Likelihood......Page 92
5 SIMPLE BAYESIAN MODELS......Page 94
5.1 Bayes’ Theorem......Page 96
5.2 The Relationship between Likelihood and Bayes’......Page 100
5.3 Finding the Posterior Distribution in Closed Form......Page 101
5.4 More about Prior Distributions......Page 105
6 HIERARCHICAL BAYESIAN MODELS......Page 122
6.1 What Is a Hierarchical Model?......Page 123
6.2 Example Hierarchical Models......Page 124
6.3 When Are Observation and Process Variance Identifiable?......Page 156
II Implementation......Page 158
7.1 Overview......Page 160
7.2 How Does MCMC Work?......Page 161
7.3 Specifics of the MCMC Algorithm......Page 165
7.4 MCMC in Practice......Page 192
8.1 Model Checking......Page 196
8.2 Marginal Posterior Distributions......Page 205
8.3 Derived Quantities......Page 209
8.4 Predictions of Unobserved Quantities......Page 211
8.5 Return to the Wildebeest......Page 216
9 INFERENCE FROM MULTIPLE MODELS......Page 224
9.1 Model Selection......Page 225
9.2 Model Probabilities and Model Averaging......Page 237
9.3 Which Method to Use?......Page 242
III Practice in Model Building......Page 246
10.1 A General Approach......Page 248
10.2 An Example of Model Building: Aboveground Net Primary Production in Sagebrush Steppe......Page 252
11 PROBLEMS......Page 258
11.1 Fisher’s Ticks......Page 259
11.2 Light Limitation of Trees......Page 260
11.3 Landscape Occupancy of Swiss Breeding Birds......Page 261
11.4 Allometry of Savanna Trees......Page 262
11.5 Movement of Seals in the North Atlantic......Page 263
12.1 Fisher’s Ticks......Page 266
12.2 Light Limitation of Trees......Page 271
12.3 Landscape Occupancy of Swiss Breeding Birds......Page 274
12.4 Allometry of Savanna Trees......Page 279
12.5 Movement of Seals in the North Atlantic......Page 283
Afterword......Page 288
Acknowledgments......Page 292
A Probability Distributions and Conjugate Priors......Page 294
Bibliography......Page 298
Index......Page 308