An approximate Bayesian marginal likelihood approach for estimating nite mixtures

Estimation of nite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirich- let prior model, a computationally e cient stochastic approximation version of the marginal likelihood is proposed and large-sample theory is presented. By restricting the support to a nite grid, a simulated annealing method is employed to maximize the marginal likelihood and estimate the support. Real and simulated data exam- ples show that this novel stochastic approximation{simulated annealing procedure compares favorably to existing methods.