Stick-Breaking Representation and Computation for Normalized Generalized Gamma Processes

Using fractions of gamma and exponentially titled stable random variables this article develops a stick-breaking representation of a truncated normalized generalized gamma process. Sampling from the posterior of this process requires sampling from gamma titled stable random variables and we develop...

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Bibliographic Details
Published inSankhya. Series. A Vol. 77; no. 2; pp. 300 - 329
Main Authors Lau, John W., Cripps, Edward
Format Journal Article
LanguageEnglish
Published New Delhi Springer 01.08.2015
Springer India
Indian Statistical Institute
Subjects
Algorithms
Bayesian analysis
Fractions
Mathematics and Statistics
Open source software
Random variables
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Stick-breaking representation
Bayesian nonparametrics
Normalized generalized gamma process
Primary 62F15; Secondary 60G55, 62G07
Gamma titled stable random variable
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Summary:Using fractions of gamma and exponentially titled stable random variables this article develops a stick-breaking representation of a truncated normalized generalized gamma process. Sampling from the posterior of this process requires sampling from gamma titled stable random variables and we develop an algorithm to do so that is readily implemented in the open source software R. A Blocked Gibbs sampling algorithm for a Bayesian kernel mixture model is then described and we compare the performance of our algorithm with an algorithm recently proposed in the literature.
ISSN:0976-836X
0976-8378
DOI:10.1007/s13171-015-0070-y