Bayesian Models: A Statistical Primer for Ecologists

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

• Publisher: Princeton University Press
• Year: 2015
• Tongue: English
• Leaves: 314
• Edition: Course Book
• 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 Models is 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

Contents
Preface
I Fundamentals
1 PREVIEW
1.1 A Line of Inference for Ecology
1.2 An Example Hierarchical Model
1.3 What Lies Ahead?
2 DETERMINISTIC MODELS
2.1 Modeling Styles in Ecology
2.2 A Few Good Functions
3 PRINCIPLES OF PROBABILITY
3.1 Why Bother with First Principles?
3.2 Rules of Probability
3.3 Factoring Joint Probabilities
3.4 Probability Distributions
4 LIKELIHOOD
4.1 Likelihood Functions
4.2 Likelihood Profiles
4.3 Maximum Likelihood
4.4 The Use of Prior Information in Maximum Likelihood
5 SIMPLE BAYESIAN MODELS
5.1 Bayes’ Theorem
5.2 The Relationship between Likelihood and Bayes’
5.3 Finding the Posterior Distribution in Closed Form
5.4 More about Prior Distributions
6 HIERARCHICAL BAYESIAN MODELS
6.1 What Is a Hierarchical Model?
6.2 Example Hierarchical Models
6.3 When Are Observation and Process Variance Identifiable?
II Implementation
7 MARKOV CHAIN MONTE CARLO
7.1 Overview
7.2 How Does MCMC Work?
7.3 Specifics of the MCMC Algorithm
7.4 MCMC in Practice
8 INFERENCE FROM A SINGLE MODEL
8.1 Model Checking
8.2 Marginal Posterior Distributions
8.3 Derived Quantities
8.4 Predictions of Unobserved Quantities
8.5 Return to the Wildebeest
9 INFERENCE FROM MULTIPLE MODELS
9.1 Model Selection
9.2 Model Probabilities and Model Averaging
9.3 Which Method to Use?
III Practice in Model Building
10 WRITING BAYESIAN MODELS
10.1 A General Approach
10.2 An Example of Model Building: Aboveground Net Primary Production in Sagebrush Steppe
11 PROBLEMS
11.1 Fisher’s Ticks
11.2 Light Limitation of Trees
11.3 Landscape Occupancy of Swiss Breeding Birds
11.4 Allometry of Savanna Trees
11.5 Movement of Seals in the North Atlantic
12 SOLUTIONS
12.1 Fisher’s Ticks
12.2 Light Limitation of Trees
12.3 Landscape Occupancy of Swiss Breeding Birds
12.4 Allometry of Savanna Trees
12.5 Movement of Seals in the North Atlantic
Afterword
Acknowledgments
A Probability Distributions and Conjugate Priors
Bibliography
Index