A1150
Title: Nonparametric mixture models and HMMS
Authors: Judith Rousseau - University Paris Dauphine (France) [presenting]
Elisabeth Gassiat - Universite Paris-Sud, Orsay (France)
Elodie Vernet - Universite Paris Sud (France)
Kerrie Mengersen - Queensland University of Technology (Australia)
Abstract: In the recent years some results have been obtained about the identifiability of mixture models - possibly dynamical - when the emission distributions are not specified. In particular, in the case of independent and identically distributed hidden states living on a finite state space, the parameters (emission distributions and weights of the mixture) are identifiable when each individual is associated to three independent observations. In the case of non independent hidden states, then as soon as the transition matrix is invertible, then the parameters are identifiable. We investigate estimation in these models and discuss some aspects of semi-parametric Bayesian estimation, including Bernstein von Mises theorems for the weights (or transition matrices) and estimation of the number of hidden states.
