An approximate Bayesian marginal likelihood approach for estimating finite mixtures

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.

16 pages, 1 figure, 3 tables

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• A nonparametric empirical Bayes framework for large-scale multiple testing
• Consistency of a recursive estimate of mixing distributions
• Stochastic Approximation and Newton's Estimate of a Mixing Distribution
• Semiparametric inference in mixture models with predictive recursion marginal likelihood
• Convergence rate for predictive recursion estimation of finite mixtures

Cited by in corpus (4)

• A semiparametric scale-mixture regression model and predictive recursion maximum likelihood
• Convergence rate for predictive recursion estimation of finite mixtures
• Estimating a mixing distribution on the sphere using predictive recursion
• Asymptotically optimal nonparametric empirical Bayes via predictive recursion