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Incorporating a collection of recent results, P�lya 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 P�lya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete P�lya urn scheme in Poisson processes to achieve an equivalent view in continuous time, provides heuristical arguments to connect the P�lya 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.
- Sales Rank: #2840069 in eBooks
- Published on: 2008-06-30
- Released on: 2008-06-30
- Format: Kindle eBook
Review
"P�lya 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
About the Author
HOSAM M. MAHMOUD, PhD, is a professor at The George Washington University, Washington, D.C., and the author of Evolution of Random Search Trees (also from Wiley).
Most helpful customer reviews
11 of 12 people found the following review helpful.
models for discrete probability outcomes
By Michael R. Chernick
Urn models have a long history in probability theory going back to the papers by Ehrenfest in 1907 and Polya and Eggenberger in 1923. Johnson and Kotz wrote the first major text on these models and their applications in 1977. Although the authors do not attempt to justify why another book on this subject is warranted, I believe that it is because of new applications in sequential clinial trials with adaptive selection (play the winner rule) and the biosciences including genetics. There have been many new results motivated by the applications particularly in the 21st century. Mahmoud's book is very similar in spirit to Johnson and Kotz but is more advanced theoretically and obviouly much more up-to-date. This can be seen also by the very extensive bibliography at the end of the book.
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