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E-grāmata: Bayesian Analysis for Population Ecology

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(University of Kent, Canterbury, UK), (Centre d'Ecologie Fonctionnelle et Evolutive - CNRS, France), (ATASS Ltd, UK), (reader in statistics at the University of St. Andrews and a former EPSRC post-doctoral Research Fellow)
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Bayesian Analysis for Population EcologyPalielināt
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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 books 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.

Recenzijas

"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 ecologists statistical bookshelf. As the authors 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

Acknowledgments xi
Preface xiii
I Introduction to Statistical Analysis of Ecological Data 1
1 Introduction
3
1.1 Population Ecology
3
1.2 Conservation and Management
3
1.3 Data and Models
4
1.4 Bayesian and Classical Statistical Inference
6
1.5 Senescence
9
1.6 Summary
11
1.7 Further Reading
11
1.8 Exercises
12
2 Data, Models and Likelihoods
15
2.1 Introduction
15
2.2 Population Data
15
2.3 Modelling Survival
21
2.4 Multi-Site, Multi-State and Movement Data
28
2.5 Covariates and Large Data Sets; Senescence
30
2.6 Combining Information
33
2.7 Modelling Productivity
35
2.8 Parameter Redundancy
36
2.9 Summary
40
2.10 Further Reading
40
2.11 Exercises
42
3 Classical Inference Based on Likelihood
49
3.1 Introduction
49
3.2 Simple Likelihoods
49
3.3 Model Selection
51
3.4 Maximising Log-Likelihoods
56
3.5 Confidence Regions
57
3.6 Computer Packages
58
3.7 Summary
61
3.8 Further Reading
62
3.9 Exercises
62
II Bayesian Techniques and Tools 67
4 Bayesian Inference
69
4.1 Introduction
69
4.2 Prior Selection and Elicitation
75
4.3 Prior Sensitivity Analyses
80
4.4 Summarising Posterior Distributions
85
4.5 Directed Acyclic Graphs
89
4.6 Summary
93
4.7 Further Reading
95
4.8 Exercises
96
5 Markov Chain Monte Carlo
99
5.1 Monte Carlo Integration
99
5.2 Markov Chains
101
5.3 Markov Chain Monte Carlo
101
5.4 Implementing MCMC
124
5.5 Summary
141
5.6 Further Reading
141
5.7 Exercises
142
6 Model Discrimination
147
6.1 Introduction
147
6.2 Bayesian Model Discrimination
148
6.3 Estimating Posterior Model Probabilities
152
6.4 Prior Sensitivity
170
6.5 Model Averaging
172
6.6 Marginal Posterior Distributions
176
6.7 Assessing Temporal/Age Dependence
178
6.8 Improving and Checking Performance
189
6.9 Additional Computational Techniques
192
6.10 Summary
193
6.11 Further Reading
194
6.12 Exercises
195
7 MCMC and RJMCMC Computer Programs
199
7.1 R Code (MCMC) for Dipper Data
199
7.2 WinBUGS Code (MCMC) for Dipper Data
205
7.3 MCMC within the Computer Package MARK
209
7.4 R code (RJMCMC) for Model Uncertainty
213
7.5 WinBUGS Code (RJMCMC) for Model Uncertainty
226
7.6 Summary
231
7.7 Further Reading
232
7.8 Exercises
233
III Ecological Applications 239
8 Covariates, Missing Values and Random Effects
241
8.1 Introduction
241
8.2 Covariates
242
8.3 Missing Values
251
8.4 Assessing Covariate Dependence
259
8.5 Random Effects
264
8.6 Prediction
270
8.7 Splines
270
8.8 Summary
273
8.9 Further Reading
274
9 Multi-State Models
277
9.1 Introduction
277
9.2 Missing Covariate/Auxiliary Variable Approach
277
9.3 Model Discrimination and Averaging
286
9.4 Summary
303
9.5 Further Reading
304
10 State-Space Modelling
307
10.1 Introduction
307
10.2 Leslie Matrix-Based Models
314
10.3 Non-Leslie-Based Models
332
10.4 Capture-Recapture Data
339
10.5 Summary
342
10.6 Further Reading
342
11 Closed Populations
345
11.1 Introduction
345
11.2 Models and Notation
346
11.3 Model Fitting
347
11.4 Model Discrimination and Averaging
354
11.5 Line Transects
356
11.6 Summary
359
11.7 Further Reading
360
Appendices 363
A Common Distributions
365
A.1 Discrete Distributions
365
A.2 Continuous Distributions
368
B Programming in R
375
B.1 Getting Started in R
375
B.2 Useful R Commands
376
B.3 Writing (RJ)MCMC Functions
378
B.4 R Code for Model C/C
379
B.5 R Code for White Stork Covariate Analysis
387
B.6 Summary
398
C Programming in WinBUGS
401
C.1 WinBUGS
401
C.2 Calling WinBUGS from R
410
C.3 Summary
415
References 417
Index 435
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.
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