E. Moreno
Bayesian clustering k random samples is a model selection problem in the class of product partition models, and this talk studies the asymptotic of the posterior distribution of the clusters when k =O(n^a) for 0 ≤a ≤ 1.
We examine the asymptotic for four model priors: the hierarchical uniform prior, the Ewens-Pitman prior, the Jensen-Liu prior and the uniform prior.
We prove that when sampling from a p−clusters model, posterior model consistency holds for both the hierarchical uniform prior and the Ewens-Pitman prior when a is in a subset of [0,1] that depends on p. For the Jensen-Liu prior and the uniform prior the procedure is inconsistent for any a and p ≥ 1.
We also find that the rate of convergence to one of the posterior probability of the true cluster model is larger for the hierarchical uniform prior than for the Ewens-Pitman prior.
Palabras clave / Keywords: clustering, posterior model consistency, product partition model
Programado
Sesión GT02-4: Análisis Multivariante y Clasificación (AMyC-4). Organizadora: Eva Boj del Val
29 de mayo de 2018 17:00
Sala 5
