The Annals of Applied Probability

A Fleming–Viot process and Bayesian nonparametrics

Stephen G. Walker, Spyridon J. Hatjispyros, and Theodoros Nicoleris

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Abstract

This paper provides a construction of a Fleming–Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of the Gibbs sampler based Markov processes. In particular, we concentrate on the Chapman–Kolmogorov consistency conditions which allows a simple derivation of such a Fleming–Viot process, once a key and apparently new combinatorial result for Pólya-urn sequences has been established.

Article information

Source
Ann. Appl. Probab., Volume 17, Number 1 (2007), 67-80.

Dates
First available in Project Euclid: 13 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1171377177

Digital Object Identifier
doi:10.1214/105051606000000600

Mathematical Reviews number (MathSciNet)
MR2292580

Zentralblatt MATH identifier
1131.60045

Subjects
Primary: 60G57: Random measures 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
Secondary: 60J60: Diffusion processes [See also 58J65] 92D15: Problems related to evolution

Keywords
Chapman–Kolmogorov diffusion process Dirichlet process Pólya-urn scheme population genetics

Citation

Walker, Stephen G.; Hatjispyros, Spyridon J.; Nicoleris, Theodoros. A Fleming–Viot process and Bayesian nonparametrics. Ann. Appl. Probab. 17 (2007), no. 1, 67--80. doi:10.1214/105051606000000600. https://projecteuclid.org/euclid.aoap/1171377177


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