Introduction to WinBUGS for Ecologists book cover

Introduction to WinBUGS for Ecologists

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.

Audience
Ecologists, upper-level graduate and graduate ecology students.

Paperback, 320 Pages

Published: June 2010

Imprint: Academic Press

ISBN: 978-0-12-378605-0

Reviews

  • "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


Contents


  • 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. Normal One-Way ANOVA

    9.1 Introduction: Fixed and Random Effects

    9.2 Fixed-Effects ANOVA

    9.3 Random-Effects ANOVA

    9.4 Summary

    10. Normal Two-Way ANOVA

    10.1 Introduction: Main and Interaction Effects

    10.2 Data Generation

    10.3 Aside: Using Simulation to Assess Bias and Precision of an Estimator

    10.4 Analysis Using R

    10.5 Analysis Using WinBUGS

    10.6 Summary

    11. General Linear Model (ANCOVA)

    11.1 Introduction

    11.2 Data Generation

    11.3 Analysis Using R

    11.4 Analysis Using WinBUGS (and a Cautionary Tale About the Importance of Covariate Standardization)

    11.5 Summary

    12. Linear Mixed-Effects Model

    12.1 Introduction

    12.2 Data Generation

    12.3 Analysis Under a Random-Intercepts Model

    12.4 Analysis Under a Random-Coefficients Model without Correlation between Intercept and Slope

    12.5 The Random-Coefficients Model with Correlation between Intercept and Slope

    12.6 Summary

    13. Introduction to the Generalized Linear Model: Poisson “t-test”

    13.1 Introduction

    13.2 An Important but Often Forgotten Issue with Count Data

    13.3 Data Generation

    13.4 Analysis Using R

    13.5 Analysis Using WinBUGS

    13.6 Summary

    14. Overdispersion, Zero-Inflation, and Offsets in the GLM

    14.1 Overdispersion

    14.2 Zero-Inflation

    14.3 Offsets

    14.4 Summary

    15. Poisson ANCOVA

    15.1 Introduction

    15.2 Data Generation

    15.3 Analysis Using R

    15.4 Analysis Using WinBUGS

    15.5 Summary

    16. Poisson Mixed-Effects Model (Poisson GLMM)

    16.1 Introduction

    16.2 Data Generation

    16.3 Analysis Under a Random-Coefficients Model

    16.4 Summary

    17. Binomial “t-Test”

    17.1 Introduction

    17.2 Data Generation

    17.3 Analysis Using R

    17.4 Analysis Using WinBUGS

    17.5 Summary

    18. Binomial Analysis of Covariance

    18.1 Introduction

    18.2 Data Generation

    18.3 Analysis Using R

    18.4 Analysis Using WinBUGS

    18.5 Summary

    19. Binomial Mixed-Effects Model (Binomial GLMM)

    19.1 Introduction

    19.2 Data Generation

    19.3 Analysis Under a Random-Coefficients Model

    19.4 Summary

    20. Nonstandard GLMMs 1: Site-Occupancy Species Distribution Model

    20.1 Introduction

    20.2 Data Generation

    20.3 Analysis Using WinBUGS

    20.4 Summary

    21. Nonstandard GLMMs 2: Binomial Mixture Model to Model Abundance

    21.1 Introduction

    21.2 Data Generation

    21.3 Analysis Using WinBUGS

    21.4 Summary

    22. Conclusions

    Appendix

    References

    Index






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