Estin1ating Bayes Factors via Posterior Simulation with the Laplace-Metropolis Estin1ator

The key quantity needed for Bayesian hypothesis testing and model selection is the marginal likelihood for a model, also known as the integrated likelihood, or the marginal probability of the data. In this paper we describe a way to use posterior simulation output to estimate marginal likelihoods. vVe describe the basic Laplace-Metropolis estimator for models without random effects. For models with random effects the compound Laplace-Metropolis estimator is introduced. This estimator is applied to data from the World Fertility Survey and shown to give accurate results. Batching of simulation output is used to assess the uncertainty involved in using the compound Laplace-Metropolis estimator. The method allows us to test for the effects of independent variables in a random effects model, and also to test for the presence of random effects. \VORDS: Laplace-Metropolis estimator; Random effects models; Marginal likelihoods; l-'"cTe.Y"u,, · Cll111ll1(],'ulVJeJ, World Survey