Objective parametric model selection procedures from a Bayesian nonparametric perspective

In this paper we propose objective Bayes procedures for model selection. To this end, we follow Gutiérrez-Peña and Walker [Gutiérrez-Peña, E., Walker, S.G., 2005. Statistical decision problems and Bayesian nonparametric methods. International Statistical Review 73, 309-330], who view traditional parametric procedures as statistical decision problems where the uncertainty on the unknown model generating the observations is modelled nonparametrically. In contrast with some of the competing methods, our proposals are not affected by the lack of propriety of the prior distribution. We compare the proposed procedures with other objective methods through a simple yet challenging example. Finally, we present a simulation study and introduce a 'mosaic plot' which is useful to summarise the output of our simulations.