Bayesian Variable Selection in Regression Models using The Laplace Approximation.

The Bayesian variable selection analysis is widely used as a new methodology in air quality control trials and generalized linear models. One of the important and, of course, controversial topics in this area is selection of prior distribution of unknown model parameters. The aim of this study is presenting a substitution for mixture of priors which besides preservation of benefits and computational efficiencies obviate the available paradoxes and contradictions. In this research we pay attention to two points of view; empirical and fully Bayesian. Especially, a mixture of priors and its theoretical characteristics is introduced. Finally, the proposed model is illustrated with a real example.

Keywords:

Bayesian Variable Selection , Mixture of Priors , Bartlett’s Paradox , Information Paradox , Empirical Bayesian analysis