Polya Urn Models

Hosam Mahmoud, Jim Zidek (University of British Columbia, Vancouver, Canada), Bradley. P. Carlin (University of Minnesota, Minneapolis, Minnesota, USA) , Martin A. Tanner (Northwestern University, Evanston, Illinois, USA)

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English

CRC Press
21 January 2023

Probability & statistics

Series: Chapman & Hall/CRC Texts in Statistical Science

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.

By: Hosam Mahmoud
Series edited by: Jim Zidek (University of British Columbia Vancouver Canada), Bradley. P. Carlin (University of Minnesota, Minneapolis, Minnesota, USA), Martin A. Tanner (Northwestern University, Evanston, Illinois, USA), Julian J. Faraway (University of Bath, United Kingdom)
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 440g
ISBN: 9781032477794
ISBN 10: 1032477792
Series: Chapman & Hall/CRC Texts in Statistical Science
Pages: 306
Publication Date: 21 January 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Hosam Mahmoud

Reviews for Polya Urn Models

Polya Urn Models describes the established theory and details numerous new developments since the seminal 1977 text Urn Models and Their Application: An Approach to Modern Discrete Probability Theory by Johnson and Kotz. ... the second half of Mahmoud's book largely covers new advances since Johnson and Kotz's book ... This latter material makes the current text unique. ... The end-of-chapter exercises (of greatly varying difficulty) have excellent in-depth solutions at the end of the text. ... The book is exceptionally well written, concise, and compelling. The author obviously commands this material, and his enthusiasm is unmistakable. -Matthew Bognar, Journal of the American Statistical Association, September 2014, Vol. 109