Bayesian Core: A Practical Approach to Computational Bayesian Statistics

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Springer Science & Business Media, Feb 6, 2007 - Computers - 255 pages
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This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. While R programs are provided on the book website and R hints are given in the computational sections of the book, The Bayesian Core requires no knowledge of the R language and it can be read and used with any other programming language.

The Bayesian Core can be used as a textbook at both undergraduate and graduate levels, as exemplified by courses given at Université Paris Dauphine (France), University of Canterbury (New Zealand), and University of British Columbia (Canada). It serves as a unique textbook for a service course for scientists aiming at analyzing data the Bayesian way as well as an introductory course on Bayesian statistics. The prerequisites for the book are a basic knowledge of probability theory and of statistics. Methodological and data-based exercises are included within the main text and students are expected to solve them as they read the book. Those exercises can obviously serve as assignments, as was done in the above courses. Datasets, R codes and course slides all are available on the book website.

Jean-Michel Marin is currently senior researcher at INRIA, the French Computer Science research institute, and located at Université Paris-Sud, Orsay. He has previously been Assistant Professor at Université Paris Dauphine for four years. He has written numerous papers on Bayesian methodology and computing, and is currently a member of the council of the French Statistical Society.

Christian Robert is Professor of Statistics at Université Paris Dauphine and Head of the Statistics Research Laboratory at CREST-INSEE, Paris. He has written over a hundred papers on Bayesian Statistics and computational methods and is the author or co-author of seven books on those topics, including The Bayesian Choice (Springer, 2001), winner of the ISBA DeGroot Prize in 2004. He is a Fellow and member of the council of the Institute of Mathematical Statistics, and a Fellow and member of the research committee of the Royal Statistical Society. He is currently co-editor of the Journal of the Royal Statistical Society, Series B, after taking part in the editorial boards of the Journal of the American Statistical Society, the Annals of Statistics, Statistical Science, and Bayesian Analysis. He is also the winner of the Young Statistician prize of the Paris Statistical Society in 1996 and a recipient of an Erskine Fellowship from the University of Canterbury (NZ) in 2006.

 

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Contents

Users Manual
1
11 Expectations
2
12 Prerequisites and Further Reading
3
13 Styles and Fonts
4
14 A Short Introduction to R
6
141 R Objects
7
142 Probability Distributions in R
10
143 Writing New R Functions
11
433 About Informative Prior Analyses
104
44 The Logit Model
106
45 LogLinear Models
109
452 Inference Under a Flat Prior
113
453 Model Choice and Significance of the Parameters
114
CaptureRecapture Experiments
119
51 Inference in a Finite Population
120
52 Sampling Models
121

144 Input and Output in R
13
Normal Models
15
21 Normal Modeling
16
22 The Bayesian Toolkit
19
222 Prior Distributions
20
223 Confidence Intervals
25
23 Testing Hypotheses
27
231 ZeroOne Decisions
28
232 The Bayes Factor
29
233 The Ban on Improper Priors
32
24 Monte Carlo Methods
35
25 Normal Extensions
43
252 Outliers
44
Regression and Variable Selection
47
31 Linear Dependence
48
311 Linear Models
50
312 Classical Estimators
51
32 FirstLevel Prior Analysis
54
322 Zellners GPrior
58
33 Noninformative Prior Analyses
65
332 Zellners Noninformative GPrior
67
34 Markov Chain Monte Carlo Methods
70
341 Conditionals
71
342 TwoStage Gibbs Sampler
72
343 The General Gibbs Sampler
76
35 Variable Selection
77
352 FirstLevel GPrior Distribution
78
353 Noninformative Prior Distribution
80
354 A Stochastic Search for the Most Likely Model
81
Generalized Linear Models
85
41 A Generalization of the Linear Model
86
412 Link Functions
88
42 MetropolisHastings Algorithms
91
422 The Independence Sampler
92
423 The Random Walk Sampler
93
424 Output Analysis and Proposal Design
94
43 The Probit Model
98
432 Noninformative GPriors
101
522 The TwoStage CaptureRecapture Model
123
523 The TStage CaptureRecapture Model
127
53 Open Populations
131
54 AcceptReject Algorithms
135
55 The ArnasonSchwarz CaptureRecapture Model
138
551 Modeling
139
552 Gibbs Sampler
142
Mixture Models
147
61 Introduction
148
63 MCMC Solutions
154
64 Label Switching Difficulty
162
65 Prior Selection
166
66 Tempering
167
67 Variable Dimension Models
170
671 Reversible Jump MCMC
171
672 Reversible Jump for Normal Mixtures
174
673 Model Averaging
179
Dynamic Models
182
71 Dependent Data
184
72 Time Series Models
188
722 MA Models
197
723 StateSpace Representation of Time Series Models
201
724 ARMA Models
203
73 Hidden Markov Models
204
731 Basics
205
732 ForwardBackward Representation
210
Image Analysis
217
81 Image Analysis as a Statistical Problem
218
822 A Probabilistic Version of the knn Methodology
220
823 MCMC Implementation
224
83 Image Segmentation
227
831 Markov Random Fields
228
832 Ising and Potts Models
232
833 Posterior Inference
237
References
247
Index
250
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About the author (2007)

Robert, CREST-INSEE, Paris, France.