Marin J.-M., Robert C. Bayesian Core: A Practical Approach to Computational Bayesian Statistics

Springer – 2007, 258 pages
ISBN: 0387389792This 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.User’s Manual
Expectations
Prerequisites and Further Reading
Styles and Fonts
A Short Introductionto R
R Objects
Probability Distributions in R
Writing New R Functions
Input and Output in R
Administration of R Objects
Normal Models
Normal Modeling
The Bayesian Toolkit
Bases
Prior Distributions
Confidence Intervals
Testing Hypotheses
Zero–One Decisions
The Bayes Factor
The Banon Improper Priors
Monte Carlo Methods
Normal Extensions
Prediction
Outliers
Regression and Variable Selection
Linear Dependence
Linear Models
Classical Estimators
First- Level Prior Analysis
Conjugate Priors
Zellner’s G-Prior
Noninformative Prior Analyses
Jeffreys’ Prior
Zellner’s Noninformative G-Prior
Markov Chain Monte Carlo Methods
Conditionals
Two-Stage Gibbs Sampler
The General Gibbs Sampler
Variable Selection
Decisional Setting
First-Level G-Prior Distribution
Noninformative Prior Distribution
A Stochastic Search for the MostLikely Model
Generalized Linear Models
A Generalization of the Linear Model
Motivation
Link Functions
Metropolis–Hastings Algorithms
Definition
The Independence Sampler
The Random Walk Sampler
Output Analysisand Proposal Design
The Probit Model
Flat Prior
Noninformative G-Priors
About Informative Prior Analyses
The Logit Model
Log-Linear Models
Contingency Tables
Inference Undera Flat Prior
Model Choiceand Significance of the Parameters
Capture–Recapture Experiments
Inference in a Finite Population
Sampling Models
The Binomial Capture Model
The Two-Stage Capture–Recapture Model
The T-Stage Capture–Recapture Model
Open Populations
Accept–Reject Algorithms
The Arnason–Schwarz Capture–Recapture Model
Modeling
Gibbs Sampler
Mixture ModelsFinite Mixture Models
MCMC Solutions
Label Switching Difficulty
Prior Selection
Tempering
Variable Dimension Models
Reversible Jump MCMC
Reversible Jump for Normal Mixtures
Model Averaging
Dynamic Models.
Dependent Data
Time Series Models
AR Models
MA Models
State–Space Representation of Time Series Models
ARMA Models
Hidden Markov Models
Basics
Forward–Backward Representation
Image Analysis
Image Analysisasa Statistical Problem
Computer Visionand Classification
Thek-Nearest-Neighbor Method
A Probabilistic Version of the knn Methodology
MCMC Implementation
Image Segmentation
Markov Random Fields
Isingand Potts Models
Posterior Inference