A Comparison of Marginal Likelihood Computation Methods

In a Bayesian analysis, different models can be compared on the basis of the expected or marginal likelihood they attain. Many methods have been devised to compute the marginal likelihood, but simplicity is not the strongest point of most methods. At the same time, the precision of methods is often questionable. In this paper several methods are presented in a common framework. The explanation of the differences is followed by an application, in which the precision of the methods is tested on a simple regression model where a comparison with analytical results is possible.