The Annals of Statistics

Poisson calculus for spatial neutral to the right processes

Lancelot F. James

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 34, Number 1 (2006), 416-440.

Dates
First available in Project Euclid: 2 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1146576269

Digital Object Identifier
doi:10.1214/009053605000000732

Mathematical Reviews number (MathSciNet)
MR2275248

Zentralblatt MATH identifier
1091.62012

Subjects
Primary: 62G05: Estimation
Secondary: 62F15: Bayesian inference

Keywords
Bayesian nonparametrics inhomogeneous Poisson process Lévy processes neutral to the right processes regenerative compositions survival analysis

Citation

James, Lancelot F. Poisson calculus for spatial neutral to the right processes. Ann. Statist. 34 (2006), no. 1, 416--440. doi:10.1214/009053605000000732. https://projecteuclid.org/euclid.aos/1146576269


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