E. Moreno Bas, F. J. Girón González-Torre
Clustering k samples is a model selection problem for which we develop a product partition model for the case k=O(n^{a}) , 0≤a≤1, where n denotes the sample size of each sample.
While the choice of the prior on the model parameters is not relevant for the consistency of the procedure, the choice of the prior on the model space is of utmost importance, almost overshadowing the other parts of the clustering problem. We examine the asymptotic behavior of the posterior model probabilities based on two priors on the models, the hierarchical uniform (HU) prior and the Ewens-Pitman (EP) prior.
We give sufficient conditions on the rate of grow of k to ensure that as n→∞ posterior model consistency holds for both the HU prior and the EP prior. We also find that the rate of convergence to one of the posterior probability of the true model is faster for the HU than for the EP prior.
Palabras clave: Bayesian model selection, clustering, Ewens-Pitman prior, hierarchical uniform prior, intrinsic prior, posterior model consistency, product partition model.
Programado
L06.2 Grupo de Inferencia Bayesiana: Bayesian model selection in Classification and Clustering
5 de septiembre de 2016 12:55
0.09 - Aula de proyectos 2
