Approximate reference priors in the presence of latent structures

We propose and illustrate a novel approach for deriving reference priors when the statistical model can be expressed via a stochastic representation or a latent structure. Given a parametric model, it is well known that, under general regularity conditions, both Jeffreys' and Berger and Bernardo's methods of producing objective priors are based on the expected Fisher information matrix. We refer to situations where the direct calculation of the expected Fisher information matrix and the subsequent computation of the objective priors are difficult. The solution proposed is based on the completion idea, already exploited in Bayesian computational strategies. The method is illustrated via examples of general interest. A possible generalization to the case of models with nuisance parameters is also described.