# Introduction to WinBUGS for Ecologists

## 1st Edition

**Bayesian approach to regression, ANOVA, mixed models and related analyses**

**Bayesian approach to regression, ANOVA, mixed models and related analyses**

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)

Ecologists, upper-level graduate and graduate ecology students.

Foreword
Preface
1. Introduction
1.1 Advantages of the Bayesian Approach to Statistics
1.2 So Why Then Isn’t Everyone a Bayesian?
1.3 WinBUGS
1.4 Why This Book?
1.5 What This Book Is Not About: Theory of Bayesian Statistics and Computation
1.6 Further Reading
1.7 Summary
2. Introduction to the Bayesian Analysis of a Statistical Model
2.1 Probability Theory and Statistics
2.2 Two Views of Statistics: Classical and Bayesian
2.3 The Importance of Modern Algorithms and Computers for Bayesian Statistics
2.4 Markov chain Monte Carlo (MCMC) and Gibbs Sampling
2.5 What Comes after MCMC?
2.6 Some Shared Challenges in the Bayesian and the Classical Analysis of a Statistical Model
2.7 Pointer to Special Topics in This Book
2.8 Summary
3. WinBUGS
3.1 What Is WinBUGS?
3.2 Running WinBUGS from R
3.3 WinBUGS Frees the Modeler in You
3.4 Some Technicalities and Conventions
4. A First Session in WinBUGS: The “Model of the Mean”
4.1 Introduction
4.2 Setting Up the Analysis
4.3 Starting the MCMC blackbox
4.4 Summarizing the Results
4.5 Summary
5. Running WinBUGS from R via R2WinBUGS
5.1 Introduction
5.2 Data Generation
5.3 Analysis Using R
5.4 Analysis Using WinBUGS
5.5 Summary
6. Key Components of (Generalized) Linear Models: Statistical Distributions and the Linear Predictor
6.1 Introduction
6.2 Stochastic Part of Linear Models: Statistical Distributions
6.3 Deterministic Part of Linear Models: Linear Predictor and Design Matrices
6.4 Summary
7. t-Test: Equal and Unequal Variances
7.1 t-Test with Equal Variances
7.2 t-Test with Unequal Variances
7.3 Summary and a Comment on the Modeling of Variances
8. Normal Linear Regression
8.1 Introduction
8.2 Data Generation
8.3 Analysis Using R
8.4 Analysis Using WinBUGS
8.5 Summary
9. Norma

- No. of pages:
- 320

- Language:
- English

- Copyright:
- © 2010

- Published:
- 17th June 2010

- Imprint:
- Academic Press

- Print ISBN:
- 9780123786050

- Electronic ISBN:
- 9780123786067

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.

Population Ecologist, Swiss Ornithological Institute, Switzerland

"I don’t believe this book was written with the goal of being treated as the primary text of an intro Bayesian statistics course. That said, it could prove to be a useful supplemental text for an introductory Bayesian course or even a linear models course. Although the book was geared towards ecologists, I believe it would be an excellent library addition for any applied modeler interested in applying Bayesian methodologies in their work."--**The American Statistician**