Bayesian model selection: a predictive approach with losses based on distances L1 and L2

A Bayesian model consists of two elements: a sampling model and a prior density. In this paper, we propose a new predictive approach for selecting a Bayesian model through a decision problem. The key idea in the paper is the loss function; we propose to measure the L1 distance (or the squared L2 distance) between the densities we can use for predicting future observations: sampling densities and posterior predictive densities. The method is also applied to the problem of variable selection in a regression model, showing a good behavior.