Title: New developments on integral priors for Bayesian model selection
Authors: Diego Salmeron Martinez - Universidad de Murcia (Spain) [presenting]
Juan Antonio Cano Sanchez - Universidad de Murcia (Spain)
Christian Robert - Universite Paris-Dauphine (France)
Abstract: Integral priors were developed for Bayesian model selection and have been successfully applied in many situations. However, two aspects deserve special attention. First, the method is stated for the comparison of two models. Second, nonparametric density estimates of the integral priors have been typically needed to approximate the Bayes factors, which translates into more computing time. We generalize the definition for more than two models and propose new numerical procedures to approximate the Bayes factors. The method is illustrated with several examples, including location-scale models, Poisson versus the negative binomal family, hypothesis testing for the exponential distribution mean, and the problem of testing if the mean of the normal distribution with unknown variance is negative, zero, or positive. Finally, we illustrate the method for the variable selection problem.