Dirichlet prior sieves in finite normal mixtures

Hemant Ishwaran, Mahmoud Zarepour

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


The use of a finite dimensional Dirichlet prior in the finite normal mixture model has the effect of acting like a Bayesian method of sieves. Posterior consistency is directly related to the dimension of the sieve and the choice of the Dirichlet parameters in the prior. We find that naive use of the popular uniform Dirichlet prior leads to an inconsistent posterior. However, a simple adjustment to the parameters in the prior induces a random probability measure that approximates the Dirichlet process and yields a posterior that is strongly consistent for the density and weakly consistent for the unknown mixing distribution. The dimension of the resulting sieve can be selected easily in practice and a simple and efficient Gibbs sampler can be used to sample the posterior of the mixing distribution.

Original languageEnglish (US)
Pages (from-to)941-963
Number of pages23
JournalStatistica Sinica
Issue number3
StatePublished - Jul 1 2002
Externally publishedYes


  • Bose-Einstein distribution
  • Dirichlet process
  • Identification
  • Method of sieves
  • Random probability measure
  • Relative entropy
  • Weak convergence

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability


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