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About this book
About this book
Bayesian model selection is a fundamental part of the Bayesian statistical modeling process. The quality of these solutions usually depends on the goodness of the constructed Bayesian model. Realizing how crucial this issue is, many researchers and practitioners have been extensively investigating the Bayesian model selection problem.
This book provides comprehensive explanations of the concepts and derivations of the Bayesian approach for model selection and related criteria, including the Bayes factor, the Bayesian information criterion (BIC), the generalized BIC, and the pseudo marginal likelihood. It also includes a wide range of practical examples of model selection criteria.
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
Tomohiro Ando is an associate professor of management science in the Graduate School of Business Administration at Keio University in Japan.