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February 2006 Poisson calculus for spatial neutral to the right processes
Lancelot F. James
Ann. Statist. 34(1): 416-440 (February 2006). DOI: 10.1214/009053605000000732

Abstract

Neutral to the right (NTR) processes were introduced by Doksum in 1974 as Bayesian priors on the class of distributions on the real line. Since that time there have been numerous applications to models that arise in survival analysis subject to possible right censoring. However, unlike the Dirichlet process, the larger class of NTR processes has not been used in a wider range of more complex statistical applications. Here, to circumvent some of these limitations, we describe a natural extension of NTR processes to arbitrary Polish spaces, which we call spatial neutral to the right processes. Our construction also leads to a new rich class of random probability measures, which we call NTR species sampling models. We show that this class contains the important two parameter extension of the Dirichlet process. We provide a posterior analysis, which yields tractable NTR analogues of the Blackwell–MacQueen distribution. Our analysis turns out to be closely related to the study of regenerative composition structures. A new computational scheme, which is an ordered variant of the general Chinese restaurant processes, is developed. This can be used to approximate complex posterior quantities. We also discuss some relationships to results that appear outside of Bayesian nonparametrics.

Citation

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Lancelot F. James. "Poisson calculus for spatial neutral to the right processes." Ann. Statist. 34 (1) 416 - 440, February 2006. https://doi.org/10.1214/009053605000000732

Information

Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62012
MathSciNet: MR2275248
Digital Object Identifier: 10.1214/009053605000000732

Subjects:
Primary: 62G05
Secondary: 62F15

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 1 • February 2006
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