Parameter Estimation For Mixture Models

In this paper, we discuss the parameter estimation for finite mixture models. First, wespecified the formal of density function p(x;θ_j) of mixed components (supposingnormal distribution, that is to say finite mixture models which we discuss is normalmixture models). Second, we specified the number g of mixed components. Finally, weestimate the parameters of finite mixture models.In this paper, we introduce the EM algorithm (including the EM algorithm ofmaximum likelihood estimation and the EM algorithm of Bayesian maximum a posterioriestimation), the MCEM algorithm and the Gibbs sampler. Bilmes J have estimated theparameters of normal mixture models with the EM algorithm of maximum likelihoodestimation. And, Figueiredo proposed that we can estimate the parameters of normalmixture models with a modified EM algorithm. In this paper, besides introducing twomethods, we estimate the parameters of normal mixture models with the EM algorithm ofBayesian maximum a posteriori estimation, the MCEM algorithm and the Gibbs sampler.Finally, we analyze an example of one-dimensional normal mixture models. Estimate theparameters of normal mixture models with the EM algorithm of maximum likelihoodestimation, the EM algorithm of Bayesian maximum a posteriori estimation, the MCEMalgorithm and the Gibbs sampler. And we compare these methods.