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MCMC Control Spreadsheets for Exponential Mixture Estimation |
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| Authors: | Marie-Anne Gruet Anne Philippe Christian P. Robert |
| Affiliation: | 1. INRA, Department of Biometrics and Artificial Intelligence , F-78352, Jouy-en-Josas, France;2. Université de Rouen de Lille I, Laboratory of Probability and Statistics , CNRS E.P. 1765, 59655 Villeneuve d'Ascq Cedex, France;3. Université de Rouen and CREST-ENSAE , 3 Avenue Pierre Larousse, 92245 Malakoff Cedex, Paris , France |
| Abstract: | Abstract This article presents Bayesian inference for exponential mixtures, including the choice of a noninformative prior based on a location-scale reparameterization of the mixture. Adapted control sheets are proposed for studying the convergence of the associated Gibbs sampler. They exhibit a strong lack of stability in the allocations of the observations to the different components of the mixture. The setup is extended to the case when the number of components in the mixture is unknown and a reversible jump MCMC technique is implemented. The results are illustrated on simulations and a real dataset. |
| Keywords: | Allocation map Central limit theorem Convergence control Gibbs sampler Normality test Reversible jump Sub-sampling |