Bayesian Methods for Ecology

Bayesian Methods for Ecology

by Michael A. McCarthy
     
 

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ISBN-10: 0521850576

ISBN-13: 9780521850575

Pub. Date: 04/28/2007

Publisher: Cambridge University Press

The interest in using Bayesian methods in ecology is increasing, but most ecologists do not know how to carry out the required analyses. This book bridges that gap. It describes Bayesian approaches to analysing averages, frequencies, regression, correlation and analysis of variance in ecology. This book also incorporates case studies to demonstrate mark-recapture

Overview

The interest in using Bayesian methods in ecology is increasing, but most ecologists do not know how to carry out the required analyses. This book bridges that gap. It describes Bayesian approaches to analysing averages, frequencies, regression, correlation and analysis of variance in ecology. This book also incorporates case studies to demonstrate mark-recapture analysis, development of population models and the use of subjective judgement. The advantages of Bayesian methods including the incorporation of any relevant prior information and the ability to assess the evidence in favour of competing hypotheses are also described here. The analyses described in this book use the freely available software, WinBUGS, and there is an accompanying website containing the data files and WinBUGS codes that are used in the book. The Bayesian methods described here will be of use to ecologists at the level of upper undergraduate.

About the Author:
Michael A. McCarthy is Senior Ecologist at the Royal Botanical Gardens, Melbourne and Senior Fellow in the School of Botany at the University of Melbourne, Australia

Product Details

ISBN-13:
9780521850575
Publisher:
Cambridge University Press
Publication date:
04/28/2007
Pages:
310
Product dimensions:
5.98(w) x 8.98(h) x 0.79(d)

Related Subjects

Table of Contents

Preface     xi
Introduction     1
Logic in determining the presence or absence of a species     4
Estimation of a mean     20
Concluding remarks     29
Critiques of statistical methods     30
Introduction     30
Sex ratio of koalas     31
Null hypothesis significance testing     35
Information-theoretic methods     45
Bayesian methods     52
Estimating effect sizes     58
Concluding remarks     61
Analysing averages and frequencies     63
The average     63
The Poisson distribution with extra variation     71
Estimating differences     71
Required sample sizes when estimating means     73
Estimating proportions     81
Multinomial models     88
Concluding remarks     92
How good are the models?     94
How good is the fit?     95
How complex is the model?     101
Combining measures of fit and simplicity     105
The Bayes factor and model probabilities     108
Evaluating the shape of distributions     116
Concluding remarks     118
Regression and correlation     119
Regression     119
Correlation     148
Concluding remarks     156
Analysis of variance     158
One-way ANOVA     158
Coding of variables     159
Fixed and random factors     162
Two-way ANOVA     165
Interaction terms in ANOVA     167
Variance partitioning     167
An example of ANOVA: effects of vegetation removal on a marsupial     170
Analysis of covariance     180
ANCOVA: a case study     182
Log-linear models for contingency tables     190
Concluding remarks     193
Case Studies
Mark-recapture analysis     197
Methods     197
Effects of marking frogs     207
Logistic regression     209
Model A     210
Models B and C     211
Population dynamics     217
Mountain pygmy possums     217
Subjective priors     225
Eliciting probabilities     225
Handling differences of opinion     226
Using subjective judgements     227
Using the consensus of experts      227
Representing differences of opinion with subjective priors     230
Using Bayesian networks to represent expert opinion     236
Concluding remarks     243
Conclusion     244
Prior information     244
Flexible statistical models     245
Intuitive results     245
Bayesian methods make us think     245
A Bayesian future for ecology     246
Appendices
A tutorial for running WinBUGS     249
A summary of steps for running WinBUGS     249
The steps in more detail     249
How to write WinBUGS code     253
Probability distributions     255
Discrete random variables     255
Continuous random variables     257
Univariate discrete distributions     261
Univariate continuous distributions     266
Multivariate discrete distributions     272
Multivariate continuous distributions     273
Conjugacy     275
MCMC algorithms     277
Why does it work?     280
References     282
Index     293

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