Bayesian Variable Selection Utilizing Posterior Probability Credible Intervals

In recent years, there has been growing interest in the problem of model selection in the Bayesian framework. Current approaches include methods based on computing model probabilities such as Stochastic Search Variable Selection (SSVS) and Bayesian LASSO and methods based on model choice criteria, such as the Deviance Information Criterion (DIC). Methods in the first group compute the posterior probabilities of models or model parameters often using a Markov Chain Monte Carlo (MCMC) technique, and select a subset of the variables based on a pre-specified threshold on the posterior probability. However, these methods rely heavily on the prior choices of parameters and the results can be highly sensitive when priors are changed. DIC is a Bayesian generalization of the Akaike9s Information Criterion (AIC) that penalizes for large number of parameters, it has the advantage that can be used for selection of mixed effect models but tend to prefer over-parameterized models. We here propose a novel variable selection algorithm that utilizes the parameters credible intervals to select the variables to be kept in the model. We will show this algorithm yields comparable or better results comparing to DIC in a simulation study, as well as implementing this algorithm in a real-world example.