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Bayesian Model Selection and Statistical Modeling

Tomohiro Ando
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
Statistics: Textbooks and Monographs
We do not plan to review this book.

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