Polya Urn Models  book cover
1st Edition

Polya Urn Models

ISBN 9781032477794
Published January 21, 2023 by CRC Press
306 Pages 11 B/W Illustrations

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Book Description

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.

Table of Contents

Urn Models and Rudiments of Discrete Probability. Some Classical Urn Problems.Pólya Urn Models.Poissonization. The Depoissonization Heuristic. Urn Schemes with Random Replacement.Analytic Urns.Applications of Pólya Urns in Informatics.Urn Schemes in Bioscience.Urns Evolving by Multiple Drawing. Answers to Exercises. Notation. Bibliographic Notes. Bibliography. Index.

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Hosam Mahmoud