On a rapid simulation of the Dirichlet process

Mahmoud Zarepour; Luai Al Labadi

doi:10.1016/j.spl.2012.01.020

On a rapid simulation of the Dirichlet process

Mahmoud Zarepour
, Luai Al Labadi

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

Abstract

We describe a simple, yet efficient, procedure for approximating the Lévy measure of a Gamma. (α, 1) random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's representation of the Dirichlet process. This approximation is written based on arrivals of a homogeneous Poisson process. We compare the efficiency of our approximation to several other well-known approximations of the Dirichlet process and demonstrate a significant improvement.

Original language	English
Pages (from-to)	916-924
Number of pages	9
Journal	Statistics and Probability Letters
Volume	82
Issue number	5
DOIs	https://doi.org/10.1016/j.spl.2012.01.020
Publication status	Published - May 2012
Externally published	Yes

Keywords

Dirichlet process
Gamma process
Lévy measure
Nonparametric Bayesian
Stick-breaking representation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2012.01.020

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title = "On a rapid simulation of the Dirichlet process",

abstract = "We describe a simple, yet efficient, procedure for approximating the L{\'e}vy measure of a Gamma. (α, 1) random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's representation of the Dirichlet process. This approximation is written based on arrivals of a homogeneous Poisson process. We compare the efficiency of our approximation to several other well-known approximations of the Dirichlet process and demonstrate a significant improvement.",

keywords = "Dirichlet process, Gamma process, L{\'e}vy measure, Nonparametric Bayesian, Stick-breaking representation",

author = "Mahmoud Zarepour and Labadi, \{Luai Al\}",

note = "Funding Information: We thank the anonymous referees and the Associate Editor for their helpful comments, which improved the paper{\textquoteright}s presentation. In addition, we extend our gratitude to Professor Raluca Balan and Professor Hemant Ishwaran for their useful suggestions. The research of the authors is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) . ",

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AU - Zarepour, Mahmoud

AU - Labadi, Luai Al

N1 - Funding Information: We thank the anonymous referees and the Associate Editor for their helpful comments, which improved the paper’s presentation. In addition, we extend our gratitude to Professor Raluca Balan and Professor Hemant Ishwaran for their useful suggestions. The research of the authors is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) .

PY - 2012/5

Y1 - 2012/5

N2 - We describe a simple, yet efficient, procedure for approximating the Lévy measure of a Gamma. (α, 1) random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's representation of the Dirichlet process. This approximation is written based on arrivals of a homogeneous Poisson process. We compare the efficiency of our approximation to several other well-known approximations of the Dirichlet process and demonstrate a significant improvement.

AB - We describe a simple, yet efficient, procedure for approximating the Lévy measure of a Gamma. (α, 1) random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's representation of the Dirichlet process. This approximation is written based on arrivals of a homogeneous Poisson process. We compare the efficiency of our approximation to several other well-known approximations of the Dirichlet process and demonstrate a significant improvement.

KW - Dirichlet process

KW - Gamma process

KW - Lévy measure

KW - Nonparametric Bayesian

KW - Stick-breaking representation

UR - https://www.scopus.com/pages/publications/84857275933

UR - https://www.scopus.com/pages/publications/84857275933#tab=citedBy

U2 - 10.1016/j.spl.2012.01.020

DO - 10.1016/j.spl.2012.01.020

M3 - Article

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SN - 0167-7152

VL - 82

SP - 916

EP - 924

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 5

ER -

On a rapid simulation of the Dirichlet process

Abstract

Keywords

ASJC Scopus subject areas

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