Model Selection With Bayes Factor Based On Markov Chain Monte Carlo Sampling

Calculating posterior probabilities and related Bayes factors for a collection of competing models has been a difficult and challenging problem for Bayesian statisticians. Bayesian model selection is to select a model correspond to reality through observation data from a number of competitive models .We know that the use of Bayes factor to select models is an important application of computing normalizing constants in statistics, but for complex or high-dimensional model, the calculation is more difficult , however, through Monte Carlo simulation is a widely used method . Markov Chain Monte Carlo (MCMC) sample is a simple and effective Bayesian method , it can deal with high dimensional calculation very well.MCMC method has been widely used for more than 50 years of history, but the development of the application in Bayesian statistics, significant test and maximum likelihood estimation is only nearly 20 years . In this paper, we first introduce the basic concept of Bayes factor, as well as the basic concepts of select models by Bayes factor; and then give the sampling process of M-H and Gibbs to select model using Bayes factor , form these methods we can avoid the computational complexity of integration with adding the model indicator as a parameter in sampling iterations ; Then for a class of linear regression model selection carried out a detailed study, results show that the use of Bayes factor with MCMC sampling can be elected "best" model, and compare with the existing criteria to select the optimal model, the two found coincident , finally, a summary of the work done.