An approximate Bayesian marginal likelihood approach for estimating finite mixtures

TL;DR

This paper introduces a novel Bayesian approach using stochastic approximation and simulated annealing to estimate finite mixture models with unknown support, demonstrating improved performance over existing methods.

Contribution

It presents a new computational method combining stochastic approximation and simulated annealing for estimating finite mixture models with unknown support, supported by large-sample theory.

Findings

Method compares favorably to existing approaches

Efficient stochastic approximation algorithm developed

Supports estimation of mixture support on finite grid

Abstract

Estimation of finite 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 Dirichlet prior model, a computationally efficient stochastic approximation version of the marginal likelihood is proposed and large-sample theory is presented. By restricting the support to a finite grid, a simulated annealing method is employed to maximize the marginal likelihood and estimate the support. Real and simulated data examples show that this novel stochastic approximation--simulated annealing procedure compares favorably to existing methods.