Analysis of mixture models using expected posterior priors, with application to classification of gamma ray bursts.

J.M. Perez and J. Berger

Consider observations distributed according to the mixture of component densities with different parameters. In the Bayesian framework, it is not possible to perform a default statistical analysis of the mixture using an improper prior for the component parameters, since the posterior distribution does not exist. To overcome this difficulty, we propose use of the expected posterior prior approach of Perez and Berger (1999). Besides providing suitable default priors for general mixture models, a key advantage of the use of expected posterior priors here is that they can be used in conjunction with Markov Chain Monte Carlo methods, even when the number of components is unknown. An application is considered involving Gamma Ray Bursts, modeled as arising from a bivariate normal mixture model with measurement errors on the observations.

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