Default Analysis of Mixture Models using Expected

Consider observations Y , distributed according to a mixture of densities Y P k j=1 w j f(j j); where 0 w j 1, P w j = 1, k and j correspond to unknown parameters of the mixture. In the a Bayesian framework, it is not possible to perform a default statistical analysis of the mixture using non-proper priors, N , for the component parameters, since the posterior distribution of these do not exist. In this work we suggest the use of the Expected Posterior Prior approach (P erez and Berger, 1999) to modify conventional, non-proper priors for j , j = 1; : : : ; k into priors that can be used for inference on the mixture model. The resulting priors have the form where m is a suitable measure over (possibly) imaginary training samples y 1 ; : : : ; y K. Both, a default and an empirical version of m are considered for the problem. The method is used for the estimation of Gamma Ray Burst, using a multivariate mixture model with errors on the observations. The estimation is done throughout a reversible jump Markov Chain Monte Carlo simulation (Green, 1995).