Bayesian Analysis for Population Ecology (Hardback)

Novel Statistical Tools for Conserving and Managing Populations

By gathering information on key demographic parameters, scientists can often predict how populations will develop in the future and relate these parameters to external influences, such as global warming. Because of their ability to easily incorporate random effects, fit state-space models, evaluate posterior model probabilities, and deal with missing data, modern Bayesian methods have become important in this area of statistical inference and forecasting.

Emphasising model choice and model averaging, Bayesian Analysis for Population Ecology presents up-to-date methods for analysing complex ecological data. Leaders in the statistical ecology field, the authors apply the theory to a wide range of actual case studies and illustrate the methods using WinBUGS and R. The computer programs and full details of the data sets are available on the book’s website.

The first part of the book focuses on models and their corresponding likelihood functions. The authors examine classical methods of inference for estimating model parameters, including maximum-likelihood estimates of parameters using numerical optimisation algorithms. After building this foundation, the authors develop the Bayesian approach for fitting models to data. They also compare Bayesian and traditional approaches to model fitting and inference.

Exploring challenging problems in population ecology, this book shows how to use the latest Bayesian methods to analyse data. It enables readers to apply the methods to their own problems with confidence.

"Although the book draws largely from questions and issues relevant to wildlife management, it serves as a useful guide for individuals outside the field. Overall, Bayesian Analysis for Population Ecology makes a great addition to a practicing ecologist’s statistical bookshelf. As the author’s state, the volume can also serve as a textbook and form a strong base for teaching an upper-division or graduate-level course in Bayesian statistics."

—Bret D. Elderd, The Quarterly Review of Biology, March 2013

"The primary strengths of this book are the authors’ extensive practical experience in applying Bayesian methods and the advanced material on model selection and multimodel inference, particularly via reversible jump Markov chain Monte Carlo. This would be a valuable reference for those already familiar with core Bayesian methods, and who are looking to learn more about ecological statistics or to implement these methods for complex ecological data. … Several fully worked examples taken mostly from the authors’ own research are presented in each chapter, and these go a long way in helping to unravel some of the art of Bayesian inference. The material is well presented and will be informative both to statisticians seeking an introduction to ecological modeling and to ecologists wishing to learn about Bayesian inference."

—Simon Bonner, Biometrics, 2011

"The book is divided into three parts. … Part 1 contains a wealth of material on aspects of such data, models analysis as well as the [historical] evolution of the subject. Part 2 is a good, self-contained introduction to Bayesian analysis … Part 3 is a collection of interesting special topics in ecological applications. … The authors write very well and illustrate with good examples. Both the technical and nontechnical discussions are good."

—International Statistical Review (2011), 79, 1

"… the book under review will be of value for quantitative ecologists. The authors offer good practical advice on the implementation of MCMC and model selection, using data types familiar to wildlife ecologists. The text includes exercises at the end of each chapter in Sections 1 and 2; these and the primers on programs R and WinBUGS are attractive features. The authors have had a leading role promoting Reversible Jump MCMC as a tool for multimodel inference in wildlife and ecological applications, and their book continues this work."

—The American Statistician, February 2011, Vol. 65, No. 1

"… a solid introduction to Bayesian modeling. … The authors have produced a text that is not only of good use to those who are analyzing population ecological data, but to anyone desiring a good overview of Bayesian modeling in general. The examples are interesting and do not hinder those not in the discipline of population ecology from understanding the explanation of the statistical principles being discussed. I recommend the book for a graduate-level course on Bayesian modeling, as well as any course related to the Bayesian modeling of population ecological data. The reader is not expected to have a prior knowledge of Bayesian modeling, nor is there an assumption that readers are familiar with R or WinBUGS. …"

—Journal of Statistical Software, August 2010, Volume 36

INTRODUCTION TO STATISTICAL ANALYSIS OF ECOLOGICAL DATA

Introduction

Population Ecology

Conservation and Management

Data and Models

Bayesian and Classical Statistical Inference

Senescence

Data, Models and Likelihoods

Introduction

Population Data

Modelling Survival

Multi-Site, Multi-State and Movement Data

Covariates and Large Data Sets; Senescence

Combining Information

Modelling Productivity

Parameter Redundancy

Classical Inference Based on the Likelihood

Introduction

Simple Likelihoods

Model Selection

Maximising Log-Likelihoods

Confidence Regions

Computer Packages

BAYESIAN TECHNIQUES AND TOOLS

Bayesian Inference

Introduction

Prior Selection and Elicitation

Prior Sensitivity Analyses

Summarising Posterior Distributions

Directed Acyclic Graphs

Markov Chain Monte Carlo

Monte Carlo Integration

Markov Chains

Markov Chain Monte Carlo (MCMC)

Implementing MCMC

Model Discrimination

Introduction

Bayesian Model Discrimination

Estimating Posterior Model Probabilities

Prior Sensitivity

Model Averaging

Marginal Posterior Distributions

Assessing Temporal/Age Dependence

Improving and Checking Performance

Additional Computational Techniques

MCMC and RJMCMC Computer Programs

R Code (MCMC) for Dipper Data

WinBUGS Code (MCMC) for Dipper Data

MCMC within the Computer Package MARK

R code (RJMCMC) for Model Uncertainty

WinBUGS Code (RJMCMC) for Model Uncertainty

ECOLOGICAL APPLICATIONS

Covariates, Missing Values and Random Effects

Introduction

Covariates

Missing Values

Assessing Covariate Dependence

Random Effects

Prediction

Splines

Multi-State Models

Introduction

Missing Covariate/Auxiliary Variable Approach

Model Discrimination and Averaging

State-Space Modelling

Introduction

Leslie Matrix-Based Models

Non-Leslie-Based Models

Capture-Recapture Data

Closed Populations

Introduction

Models and Notation

Model Fitting

Model Discrimination and Averaging

Line Transects

Appendix A: Common Distributions

Discrete Distributions

Continuous Distributions

Appendix B: Programming in R

Getting Started in R

Useful R Commands

Writing (RJ)MCMC Functions

R Code for Model C/C

R Code for White Stork Covariate Analysis

Appendix C: Programming in WinBUGS

WinBUGS

Calling WinBUGS from R

References

Index

A Summary, Further Reading, and Exercises appear at the end of most chapters.

Ruth King is a reader in statistics at the University of St. Andrews and a former EPSRC post-doctoral Research Fellow.

Byron J.T. Morgan is a professor of applied statistics at the University of Kent and co-director of the EPSRC National Centre for Statistical Ecology.

Olivier Gimenez is a research scientist in biostatistics at CNRS and a former Marie Curie research fellow.

Stephen P. Brooks is director of research at ATASS Ltd and a former professor of statistics at the University of Cambridge and EPSRC Advanced Fellow.

Bayesian Analysis for Population Ecology

By Ruth King, Byron Morgan, Olivier Gimenez, Steve Brooks

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