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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