Exact and approximate sum representations for the Dirichlet process

Hemant Ishwaran, Mahmoud Zarepour

Research output: Contribution to journalArticle

133 Citations (Scopus)

Abstract

The Dirichlet process can be regarded as a random probability measure for which the authors examine various sum representations. They consider in particular the gamma process construction of Ferguson (1973) and the "stick-breaking" construction of Sethuraman (1994). They propose a Dirichlet finite sum representation that strongly approximates the Dirichlet process. They assess the accuracy of this approximation and characterize the posterior that this new prior leads to in the context of Bayesian nonparametric hierarchical models.

Original languageEnglish
Pages (from-to)269-283
Number of pages15
JournalCanadian Journal of Statistics
Volume30
Issue number2
StatePublished - Jun 1 2002
Externally publishedYes

Fingerprint

Dirichlet Process
Random Probability Measure
Gamma Process
Bayesian Nonparametrics
Nonparametric Model
Hierarchical Model
Dirichlet
Approximation
Dirichlet process
Context
Hierarchical model
Gamma process

Keywords

  • Almost sure truncation
  • Finite dimensional Dirichlet prior
  • Lévy measure
  • Poisson process
  • Random probability measure
  • Stick-breaking prior
  • Weak convergence

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Exact and approximate sum representations for the Dirichlet process. / Ishwaran, Hemant; Zarepour, Mahmoud.

In: Canadian Journal of Statistics, Vol. 30, No. 2, 01.06.2002, p. 269-283.

Research output: Contribution to journalArticle

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