A default Bayesian test for the number of components in a mixture

A very important problem in survival analysis is the accurate selection of the relevant prognostic explanatory variables. We propose a novel approach, based on mixtures of products of Dirichlet process priors, that provides a formal inferential tool to compare the explanatory power of each covariate, in terms of the marginal likelihood attached to the induced partitions of the observations. Our proposed model is Bayesian nonparametric, and, thus, keeps the amount of model specification to a minimum, increasing robustness of the final inferences.