Polya Urn Models

Hosam Mahmoud

June 30, 2008 by Chapman and Hall/CRC
Reference - 312 Pages - 11 B/W Illustrations
ISBN 9781420059830 - CAT# C5983
Series: Chapman & Hall/CRC Texts in Statistical Science


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  • Collects recent results in Pólya urn theory
  • Looks at how some classical problems of discrete probability, such as Banach’s matchbox problem, have roots in urn models
  • Covers the Pólya–Eggenberger, Bernard Friedman’s, the Bagchi–Pal, and the Ehrenfest urns
  • Explains the processes of poissonization and depoissonization
  • Presents applications to random trees, evolution, competitive exclusion, epidemiology, clinical trials, and random circuits
  • Includes end-of-chapter exercises that range from easy to challenging, along with solutions in the back of the book that often shed more light on the topics
  • Summary

    Incorporating a collection of recent results, Pólya Urn Models deals with discrete probability through the modern and evolving urn theory and its numerous applications.

    The book first substantiates the realization of distributions with urn arguments and introduces several modern tools, including exchangeability and stochastic processes via urns. It reviews classical probability problems and presents dichromatic Pólya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete Pólya urn scheme in Poisson processes to achieve an equivalent view in continuous time, provides heuristical arguments to connect the Pólya process to the discrete urn scheme, and explores extensions and generalizations. He also discusses how functional equations for moment generating functions can be obtained and solved. The final chapters cover applications of urns to computer science and bioscience.

    Examining how urns can help conceptualize discrete probability principles, this book provides information pertinent to the modeling of dynamically evolving systems where particles come and go according to governing rules.


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