This paper surveys some well-established approaches on the approximation of
Bayes factors used in Bayesian model choice, mostly as covered in Chen et al.
(2000). 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, maximum likelihood based importance sampling,
bridge and harmonic mean sampling, as well as Chib's method based on the
exploitation of a functional equality. We demonstrate in this survey how these
different 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