Pólya urn models
著者
書誌事項
Pólya urn models
（Texts in statistical science）
CRC Press, c2009
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
Incorporating a collection of recent results, Polya 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 Polya urns as a basic discrete structure growing in discrete time. The author then embeds the discrete Polya urn scheme in Poisson processes to achieve an equivalent view in continuous time, provides heuristical arguments to connect the Polya 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.
目次
Urn Models and Rudiments of Discrete Probability. Some Classical Urn Problems.Polya Urn Models.Poissonization. The Depoissonization Heuristic. Urn Schemes with Random Replacement.Analytic Urns.Applications of Polya Urns in Informatics.Urn Schemes in Bioscience.Urns Evolving by Multiple Drawing. Answers to Exercises. Notation. Bibliographic Notes. Bibliography. Index.
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