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September 2015 Reversible Markov structures on divisible set partitions
Harry Crane, Peter McCullagh
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J. Appl. Probab. 52(3): 622-635 (September 2015). DOI: 10.1239/jap/1445543836

Abstract

We study k-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integer k = 1, 2,.... In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, for k > 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is needed to obtain a partition structure. We describe explicit Chinese restaurant-type seating rules for generating families of exchangeable k-divisible partitions that are consistent under random deletion. We further introduce the notion of Markovian partition structures, which are ensembles of exchangeable Markov chains on k-divisible partitions that are consistent under a random process of Markovian deletion. The Markov chains we study are reversible and refine the class of Markov chains introduced in Crane (2011).

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Harry Crane. Peter McCullagh. "Reversible Markov structures on divisible set partitions." J. Appl. Probab. 52 (3) 622 - 635, September 2015. https://doi.org/10.1239/jap/1445543836

Information

Published: September 2015
First available in Project Euclid: 22 October 2015

zbMATH: 1361.60010
MathSciNet: MR3414981
Digital Object Identifier: 10.1239/jap/1445543836

Subjects:
Primary: 60C05 , 60J10
Secondary: 60B99

Keywords: Chinese restaurant process , divisible partition , Ewens-Pitman partition , exchangeable partition structure , group-divisible association scheme , Markovian partition structure

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 3 • September 2015
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