## Bayesian Core: A Practical Approach to Computational Bayesian StatisticsThis 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 |

247 | |

250 | |

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Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology Andrew B. Lawson Limited preview - 2008 |