Bayesian Model Selection and Statistical Modeling

Book Preface

Bayesian model selection is a fundamental part of the Bayesian statistical modeling process. In principle, the Bayesian analysis is straightforward. Specifying the data sampling and prior distributions, a joint probability distribution is used to express the relationships between all the unknowns and the data information. Bayesian inference is implemented based on the posterior distribution, the conditional probability distribution of the unknowns given the data information. The results from the Bayesian posterior inference are then used for the decision making, forecasting, stochastic structure explorations and many other problems. However, the quality of these solutions usually depends on the quality of the constructed Bayesian models. This crucial issue has been realized by researchers and practitioners. Therefore, the Bayesian model selection problems have been extensively investigated.

A default framework for the Bayesian model selection is based on the Bayes factor, which provides the scientific foundations for various fields of natural sciences, social sciences and many other areas of study. From the Bayes factor, Bayesian information criterion (BIC), generalized Bayesian information criterion (GBIC), and various types of Bayesian model selection criteria have been proposed. One of the main objectives of this book is to provide comprehensive explanations of the concepts and derivations of the default framework for the Bayesian model selection, together with a wide range of practical examples of model selection criteria.

The Bayesian inference on a statistical model was previously complex. It is now possible to implement the various types of the Bayesian inference thanks to advances in computing technology and the use of new sampling methods, including Markov chain Monte Carlo (MCMC). Such developments together with the availability of statistical software have facilitated a rapid growth in the utilization of Bayesian statistical modeling through the computer simulations. Nonetheless, model selection is central to all Bayesian statistical modeling. There is a growing need for evaluating the Bayesian models constructed by the simulation methods.