Empirical Bayes estimation utilizing finite Gaussian Mixture Models

In this paper we develop an identification algorithm to obtain an estimation of the prior distribution in the classical problem of Bayesian inference. We consider the Empirical Bayes approach to obtain the prior distribution approximation by a finite Gaussian mixture. An Expectation-Maximization based algorithm is used to obtain an estimate of the Gaussian mixture parameters. Our approach shows a good approximation of the prior distribution when the number of experiments is increased. We illustrate the estimation performance of our proposal with numerical simulations.