New approaches to compute Bayes factor in finite mixture models

Two new approaches to estimate Bayes factors in a finite mixture model context are proposed. Specifically, two algorithms to estimate them and their errors are derived by decomposing the resulting marginal densities. Then, through Bayes factor comparisons, the appropriate number of components for the mixture model is obtained. The approaches are based on simple theory (Monte Carlo methods and cluster sampling), what makes them appealing tools in this context. The performance of both algorithms is studied for different situations and the procedures are illustrated with some previously published data sets.