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Covariances in Pólya urn schemes

Published online by Cambridge University Press:  08 October 2021

Hosam Mahmoud*
Affiliation:
Department of Statistics, The George Washington University, Washington, D.C. 20052, USA. E-mail: hosam@gwu.edu

Abstract

By now there is a solid theory for Polya urns. Finding the covariances is somewhat laborious. While these papers are “structural,” our purpose here is “computational.” We propose a practicable method for building the asymptotic covariance matrix in tenable balanced urn schemes, whereupon the asymptotic covariance matrix is obtained by solving a linear system of equations. We demonstrate the use of the method in growing tenable balanced irreducible schemes with a small index and in critical urns. In the critical case, the solution to the linear system of equations is explicit in terms of an eigenvector of the scheme.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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Footnotes

To Robert Smythe, a mentor, coauthor and friend, on his 80th birthday

References

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