### 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 language | English |
---|---|

Pages (from-to) | 269-283 |

Number of pages | 15 |

Journal | Canadian Journal of Statistics |

Volume | 30 |

Issue number | 2 |

State | Published - Jun 1 2002 |

Externally published | Yes |

### Fingerprint

### 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

*Canadian Journal of Statistics*,

*30*(2), 269-283.

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

Research output: Contribution to journal › Article

*Canadian Journal of Statistics*, vol. 30, no. 2, pp. 269-283.

}

TY - JOUR

T1 - Exact and approximate sum representations for the Dirichlet process

AU - Ishwaran, Hemant

AU - Zarepour, Mahmoud

PY - 2002/6/1

Y1 - 2002/6/1

N2 - 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.

AB - 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.

KW - Almost sure truncation

KW - Finite dimensional Dirichlet prior

KW - Lévy measure

KW - Poisson process

KW - Random probability measure

KW - Stick-breaking prior

KW - Weak convergence

UR - http://www.scopus.com/inward/record.url?scp=0036623091&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036623091&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036623091

VL - 30

SP - 269

EP - 283

JO - Canadian Journal of Statistics

JF - Canadian Journal of Statistics

SN - 0319-5724

IS - 2

ER -