Resumen del libro

Reseña: 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.

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indice: 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

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