Stochastic Approximation and Newton's Estimate of a Mixing Distribution

• Activity Number: 432
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2008 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ryan Martin*+ and Jayanta K. Ghosh
• Companies: Purdue University and Purdue University and Indian Statistical Institute
• Keywords: mixture models ; empirical Bayes ; stochastic approximation

Abstract

Recent scientific advances have increased the need for efficient methods for estimating high-dimensional mixing distributions. One major area of application is to microarray data on gene expression. In this problem, the parameters represent the effects of the individual genes and an empirical Bayes analysis proceeds by estimating the prior, or mixing distribution, based on data observed from the mixture. Newton (2002) proposed a very fast recursive algorithm for nonparametric estimation of the mixing distribution. Simulations show that this estimate performs well compared to the NPML and NP Bayes estimates, based on accuracy and computational efficiency. For finite mixtures, the algorithm is a special case of stochastic approximation (SA) and its asymptotic properties are derived from standard SA arguments, involving Lyapunov functions and ODE stability theory.