Approximate Dirichlet process computing in finite normal mixtures: Smoothing and prior information

Hemant Ishwaran, Lancelot F. James

Research output: Contribution to journalArticle

106 Scopus citations

Abstract

A rich nonparametric analysis of the finite normal mixture model is obtained by working with a precise truncation approximation of the Dirichlet process. Model fitting is carried out by a simple Gibbs sampling algorithm that directly samples the nonparametric posterior. The proposed sampler mixes well, requires no tuning parameters, and involves only draws from simple distributions, including the draw for the mass parameter that controls clustering, and the draw for the variances with the use of a nonconjugate uniform prior. Working directly with the nonparametric prior is conceptually appealing and among other things leads to graphical methods for studying the posterior mixing distribution as well as penalized MLE procedures for deriving point estimates. We discuss methods for automating selection of priors for the mean and variance components to avoid over or undersmoothing the data. We also look at the effectiveness of incorporating prior information in the form of frequentist point estimates.

Original languageEnglish (US)
Pages (from-to)508-532
Number of pages25
JournalJournal of Computational and Graphical Statistics
Volume11
Issue number3
DOIs
StatePublished - Sep 1 2002
Externally publishedYes

Keywords

  • Almost sure truncation
  • Blocked Gibbs sampler
  • Nonparametric hierarchical model
  • Penalized MLE
  • Pólya urn Gibbs sampling
  • Random probability measure

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Statistics and Probability

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