Comparing and calibrating discrepancy measures for Bayesian model selection

Abstract

Different approaches have been considered in the literatur e for the problem of Bayesian model selection. Recently, a new method was introduced and analys ed in De la Horra (2008) by minimizing the posterior expected discrepancy between the set of data and the Bayesian model, where the chi-square discrepancy was used. In this article, several discrepancy measures are considered and compared by simulation, and it is obtained th at the chi-square discrepancy is reasonable to use. Then, an easy method for calibrating disc repancies is proposed, and the behaviour of this approach is studied on simulated data. Fin ally, a set of real data is analysed