An overview is provided for the problem of calculating Bayes factors (BF) for
model selection using methods based on variants of importance sampling and
variants of Laplace Approximation, specifically path sampling (PS). These
methods are compared on several simulated and two real life data set. It is
noted that there are unexpected instabilities in PS and we provide both a
theoretical explanation and suggestions for improvement. Estimates of the same
BF may differ widely across methods.