Introduction Statistical models Bayesian statistical modeling Book organization
Introduction to Bayesian Analysis Probability and Bayes’ theorem Introduction to Bayesian analysis Bayesian inference on statistical models Sampling density specification Prior distribution Summarizing the posterior inference Bayesian inference on linear regression models Bayesian model selection problems
Asymptotic Approach for Bayesian Inference Asymptotic properties of the posterior distribution Bayesian central limit theorem Laplace method
Computational Approach for Bayesian Inference Monte Carlo integration Markov chain Monte Carlo methods for Bayesian inference Data augmentation Hierarchical modeling MCMC studies for the Bayesian inference on various types of models Noniterative computation methods for Bayesian inference
Bayesian Approach for Model Selection General framework Definition of the Bayes factor Exact calculation of the marginal likelihood Laplace’s method and asymptotic approach for computing the marginal likelihood Definition of the Bayesian information criterion Definition of the generalized Bayesian information criterion Bayes factor with improper prior Expected predictive likelihood approach for Bayesian model selection Other related topics
Simulation Approach for Computing the Marginal Likelihood Laplace–Metropolis approximation Gelfand–Day’s approximation and the harmonic mean estimator Chib’s estimator from Gibb’s sampling Chib’s estimator from MH sampling Bridge sampling methods The Savage–Dickey density ratio approach Kernel density approach Direct computation of the posterior model probabilities
Various Bayesian Model Selection Criteria Bayesian predictive information criterion Deviance information criterion A minimum posterior predictive loss approach Modified Bayesian information criterion Generalized information criterion
Theoretical Development and Comparisons Derivation of Bayesian information criteria Derivation of generalized Bayesian information criteria Derivation of Bayesian predictive information criterion Derivation of generalized information criterion Comparison of various Bayesian model selection criteria
Bayesian Model Averaging Definition of Bayesian model averaging Occam’s window method Bayesian model averaging for linear regression models Other model averaging methods
Bibliography
Index
