Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation.
The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties.
Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes 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
Laplaces 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-Days approximation and the harmonic mean estimator
Chibs estimator from Gibbs sampling
Chibs 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
Occams window method
Bayesian model averaging for linear regression models
Other model averaging methods
Bibliography
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