In empirical Bayes analysis, the estimation of the hyperparameter is entirely left to the choice of the experimenter and the corresponding empirical Bayes estimator thus fails to achieve a global coherence. In this paper, we propose a more directed approach based on the use of a formal Bayes...

Hidden Markov models lead to intricate computational problems when considered directly. In this paper, we propose an approximation method based on Gibbs sampling which allows an effective derivation of Bayes estimators for these models.

Let "π" denote an intractable probability distribution that we would like to explore. Suppose that we have a positive recurrent, irreducible Markov chain that satisfies a minorization condition and has "π" as its invariant measure. We provide a method of using simulations from the Markov chain...

A rule for choosing among nested models is presented, taking into account that the usual model selection procedure is a sequence of tests, followed by estimation of the parameters that remain in the model. We take a decision theoretical approach and formulate the loss functions and the rules...