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Examples of multivariate Markov chai...

Stanford University.

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Examples of multivariate Markov chains with orthogonal polynomial eigenfunctions.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Examples of multivariate Markov chains with orthogonal polynomial eigenfunctions./
Author:	Zhou, Hua.
Description:	168 p.
Notes:	Source: Dissertation Abstracts International, Volume: 69-10, Section: B, page: 6197.
Contained By:	Dissertation Abstracts International69-10B.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3332963
ISBN:	9780549850717

Examples of multivariate Markov chains with orthogonal polynomial eigenfunctions.
Zhou, Hua.

Examples of multivariate Markov chains with orthogonal polynomial eigenfunctions. - 168 p.

Source: Dissertation Abstracts International, Volume: 69-10, Section: B, page: 6197.

Thesis (Ph.D.)--Stanford University, 2008.

Some open problems about the Markov chains with orthogonal polynomials, or generally with polynomial eigenfunctions, are discussed and partial results presented in the final part of the thesis.

ISBN: 9780549850717Subjects--Topical Terms:

517247
Statistics.

Examples of multivariate Markov chains with orthogonal polynomial eigenfunctions.
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020 $a 9780549850717
035 $a (UMI)AAI3332963
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100 1 $a Zhou, Hua. $3 1020707
245 1 0 $a Examples of multivariate Markov chains with orthogonal polynomial eigenfunctions.
300 $a 168 p.
500 $a Source: Dissertation Abstracts International, Volume: 69-10, Section: B, page: 6197.
502 $a Thesis (Ph.D.)--Stanford University, 2008.
520 $a Some open problems about the Markov chains with orthogonal polynomials, or generally with polynomial eigenfunctions, are discussed and partial results presented in the final part of the thesis.
520 $a The Ehrenfest urn and Moran models are two canonical finite Markov chains with orthogonal polynomial eigenfunctions. This thesis studies natural generalizations of these models to the multivariate case.
520 $a In the multivariate generalization of the Ehrenfest urn model, there are N balls in d urns, where d ≥ 2 is a positive integer. At each step, a random subset of balls are chosen from the N balls and these balls change their residing urns independently according to a common stochastic matrix. The counts of balls in the urns form a multivariate chain with multinomial stationary distribution. We identify the column eigenvectors of such chains with the multivariate Krawtchouk polynomials constructed by Griffiths. Detailed knowledge of the spectral information allows for diverse applications. Our examples include the Ehrenfest chain and its variants, a recent chain studied by Hoare and Rahman, a light bulb model of Rao et al., and the coalescence problem of Tian and Liu.
520 $a The multivariate Moran model is studied in a general framework which we call the sequential Polya urn models. All Markov chains in this framework are reversible with respect to the Dirichlet-Multinomial or multivariate hypergeometric distributions and take a version of multivariate Hahn polynomials as eigenfunctions. Explicit knowledge of the eigenvalues and eigenfunctions allows us calculate the rates of convergence of these chains to their stationary distributions in chi-square distance. Specific examples include the Moran model in population genetics and its variants in community ecology, the Dirichlet-Multinomial Gibbs sampler, the multivariate Bernoulli-Laplace models and their variants.
590 $a School code: 0212.
650 4 $a Statistics. $3 517247
690 $a 0463
710 2 $a Stanford University. $3 754827
773 0 $t Dissertation Abstracts International $g 69-10B.
790 $a 0212
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3332963