Hosam Mahmoud
Polya Urn Models
Polya Urn Models
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Pólya Urn Models combines recent results from urn theory and its applications to discrete probability, covering distributions, exchangeability, stochastic processes, classical probability problems, dichromatic Pólya urns, Poisson processes, functional equations, and applications to computer science and bioscience. It helps conceptualize discrete probability principles in dynamically evolving systems.
Format: Paperback / softback
Length: 306 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd
Pólya Urn Models: A Comprehensive Introduction to Discrete Probability
Incorporating a comprehensive collection of recent results, Pólya Urn Models delves into the realm of discrete probability through the modern and evolving urn theory and its numerous applications. The book begins by substantiating the realization of distributions with urn arguments, introducing various modern tools such as exchangeability and stochastic processes via urns. It then reviews classical probability problems and presents dichromatic Pólya urns as a fundamental discrete structure that grows in discrete time.
To achieve an equivalent view in continuous time, the author embeds the discrete Pólya urn scheme within Poisson processes, providing heuristical arguments to connect the Pólya process to the discrete urn scheme. Furthermore, the book explores extensions and generalizations, discussing 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 in the modeling of dynamically evolving systems where particles come and go according to governing rules.
By exploring the versatility and power of urn models, Pólya Urn Models offers a valuable resource for researchers and practitioners in fields such as probability theory, statistics, computer science, and bioscience. It provides a solid foundation for understanding discrete probability concepts and their applications, enabling readers to apply urn theory to solve complex problems and gain insights into the behavior of dynamic systems.
Weight: 570g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032477794
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