When the number of components of a Poisson mixture distribution is unknown, one needs to make inference about it so that he might use the Gibbs sampling method to estimates the parameters of the mixture distribution. Any idea about that?
Thanks so much.
It mainly depends on the empirical context. In a ML perspective, You may use any of the several penalized likelihood criteria, say AIC, BIC, CAC, AWE and so on. In a Bayesian context, this may be either done via transdimensional algorithms, for a review, see Tardella and Petris (Canadian Journal of statistics) or via ICL, developed by the group of Celeux, Biernacki et al. In a recent paper appeared in Metron (2015, SI on latent variable models) Rastelli et al. have developed a greedy algorithm for calculating the exact ICL in a general finite mixture model.
Hello Marco,
Great! Thanks so much for your valuable information. I really appreciate your answer.
Have a nice day.
Mohamed I. Riffi
In addition to the previous answer regarding ML estimation, sometimes BIC tends to overestimate the number of clusters, so ICL is generally preferred. The R package `flexmix` can be used for this purpose. In case that the Poisson mixture contains covariates you may also have a look at the R package `poisson.glm.mix` which implements the EM algorithm under a new initialization scheme which reduces the possibility of converging to local minima. (see The Third Special Issue on Advances in Mixture Models: ``On the estimation of mixtures of Poisson regression models with large number of components'', CSDA, 2016)
Hi Panagiotis Papastamoulis,
I would like to thank you so much for your very important information regarding my answer.
I appreciate it very much.
Have a nice time.
Mohamed I. Riffi
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