Bayesian Inference

With Ecological Applications

By: Richard J Barker, William A Link

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Hardcover | 7 August 2009

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354 Pages

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24.13 x 19.68 x 2.54

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This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context.

The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists.

Engagingly written text specifically designed to demystify a complex subject
Examples drawn from ecology and wildlife research
An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference
Companion website with analytical software and examples
Leading authors with world-class reputations in ecology and biostatistics

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You Can Find This Book In

Non-Fiction Science Biology, Life Sciences Life Sciences in General Ecological Science Zoology & Animal Sciences Earth Sciences, Geography, Environment, Planning The Environment Applied Ecology Mathematics Probability & Statistics Applied Mathematics

Preface	p. xi
Acknowledgments	p. xiii
Probability and Inference
Introduction to Bayesian Inference	p. 3
Introduction	p. 3
Thomas Bayes	p. 4
The Bayesian/Frequentist Difference	p. 7
Understanding the Basis of Thomas Bayes' System of Inference	p. 8
Probability	p. 13
What is Probability?	p. 14
Basic Probability Concepts for Bayesian Inference	p. 16
Statistical Inference	p. 23
Likelihood	p. 25
Confidence Intervals	p. 29
Bayesian Interval Estimation	p. 36
Summary and Comparison of Inferential Systems	p. 42
Calculating Posterior Distributions	p. 47
Conjugacy	p. 49
Monte Carlo Methods	p. 54
Markov Chain Monte Carlo	p. 59
The Bayesian Māramatanga
Bayesian Prediction	p. 77
The Bayesian Māramatanga	p. 78
Estimating Mean Residual Lifetime	p. 81
Derived Parameters in Summary Analyses: BBS Case Study	p. 85
Derived Parameters and Out of Sample Inference in a Dose-Response Study	p. 93
Product Binomial Representation of the CJS Model	p. 98
Posterior Predictive Model Checking	p. 104
Priors	p. 109
An Example Where Priors Matter	p. 110
Objective Bayesian Inference	p. 115
Afterword	p. 123
Multimodel Inference	p. 127
The BMI Model	p. 129
Bayes Factors	p. 134
Multimodel Computation	p. 139
Indices of Model Acceptability: AIC and DIC	p. 149
Afterword	p. 157
Applications
Hidden Data Models	p. 163
Complete Data Likelihood	p. 164
Randomized Response Data	p. 165
Occupancy Models as Hierarchical Logistic Regressions	p. 176
Distance Sampling	p. 181
Finite Population Sampling	p. 186
Afterword	p. 199
Closed-Population Mark-Recapture Models	p. 201
Introduction	p. 201
Mark-Recapture Models and Missing Data	p. 202
Time and Behavior Models	p. 204
Individual Heterogeneity Models	p. 209
Example: Koalas	p. 218
Afterword	p. 223
Latent Multinomial Models	p. 225
Model M_t	p. 226
Model M_t,	p. 226
Gibbs Sampling for Model M_t,	p. 232
An Implementation of Model M_t,	p. 234
Extensions	p. 236
Open Population Models	p. 239
Continuous-Time Survival Models	p. 240
Open Population Mark-Recapture-Band-Recovery Models	p. 244
Open Population Mark-Recapture-The CJS Model	p. 247
Full Open Population Modeling Formalities	p. 252
CMSA Model and Extensions	p. 255
Multiple Groups	p. 260
Robust Design	p. 261
Multistate Models and Other Extensions of the CJS Model	p. 268
Afterword	p. 269
Individual Fitness	p. 271
Population Fitness	p. 272
Individual Fitness	p. 273
Realized Individual Fitness	p. 274
Individual Fitness in Group Context	p. 275
Analysis of Individual Fitness: An Example	p. 276
Population Summaries of Fitness	p. 281
Afterword	p. 286
Autoregressive Smoothing	p. 287
Dove Data and Preliminary Analyses	p. 288
Modeling Differences in Parameter Values	p. 291
Results for Dove Analysis	p. 292
Higher Order Differences	p. 293
Afterword	p. 295
Appendices
Probability Rules	p. 301
Properties of Moments	p. 301
Conditional Expectations	p. 303
Independence and Correlation	p. 304
Probability Distributions	p. 307
Uniform Distribution	p. 307
Discrete Uniform Distribution	p. 308
Normal Distribution	p. 308
Multivariate Normal Distribution	p. 309
Bernoulli Trials and the Binomial Distribution	p. 311
Poisson Distribution	p. 312
Multinomial Distribution	p. 313
Exponential Distribution	p. 315
Gamma Distribution	p. 317
Beta Distribution	p. 319
t-Distribution	p. 320
Negative Binomial Distribution	p. 321
Bibliography	p. 323
Index of Examples	p. 331
Index	p. 333
Table of Contents provided by Ingram. All Rights Reserved.

Bayesian Inference

With Ecological Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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