3.3 Importance sampling methods for Bayesian discrimination between embedded models (Jean-Michel Marin)

We survey some approaches on the approximation of Bayes factors used in Bayesian model choice and propose a new one. Our focus here is on methods that are based on importance sampling strategies, rather than variable dimension techniques like reversible jump MCMC, including : crude Monte Carlo, MLE based importance sampling, bridge and harmonic mean sampling, Chib?s method based on the exploitation of a functional equality, as well as a revisited Savage-Dickey?s approximation. We demonstrate in this survey how all these methods can be efficiently implemented for testing the significance of a predictive variable in a probit model. Finally, we compare their performances on a real dataset. This is a joint work with Christian P. Robert.