  Noninformative priors constructed for estimation purposes are usually not
appropriate for model selection and testing. The methodology of integral priors
was developed to get prior distributions for Bayesian model selection when
comparing two models, modifying initial improper reference priors. We propose a
generalization of this methodology to more than two models. Our approach adds
an artificial copy of each model under comparison by compactifying the
parametric space and creating an ergodic Markov chain across all models that
returns the integral priors as marginals of the stationary distribution.
Besides the garantee of their existance and the lack of paradoxes attached to
estimation reference priors, an additional advantage of this methodology is
that the simulation of this Markov chain is straightforward as it only requires
simulations of imaginary training samples for all models and from the
corresponding posterior distributions. This renders its implementation
automatic and generic, both in the nested case and in the nonnested case.
