Bayesian variable selection using hyper-g prior and adaptive sampling

Abstract

Bayesian variable selection has become an area of extensive researchthrough the last decades. The two main challenges that a researcher confronts,is the specification of the prior distribution on model parameters and thecalculation of the posterior model probability which makes the evaluation of acandidate model feasible. In linear models, popular prior choices are based onconjugate analysis of Normal-Gamma family. Among them, alternatives basedon Zellner’s g-prior are mainly preferred, as they lead to tractable marginallikelihoods. On the other hand, since posterior inference is related to highdimensional integrals, Bayesian model selection became popular only after theadoption of advanced simulation algorithms, that are used to overcomedemanding computational issues.In the current thesis, we will attempt a review of the existingmethodologies that deal with the Bayesian model selection problem. Differentways of estimating Bayes Factors will be covered and major MCMC basedalgorithms that deal with the exploration of model space and estimation ofposterior will be presented. Emphasis will be given on Bayesian adaptivesampling algorithm of Clyde et al. (2011) that exploits the idea of adaptivesampling algorithms and adopts Zellner’s g-prior to perform sampling overmodel space. Its performance will be explored both using small and largesimulated data.