Polya Urn Models (chapman & Hall/crc Texts In Statistical Science)
by Hosam Mahmoud /
2008 / English / PDF
1.7 MB Download
Incorporating a collection of recent results,
Incorporating a collection of recent results,Pólya Urn
Models
Pólya Urn
Models deals with discrete probability through the modern and
evolving urn theory and its numerous applications.
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.
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.
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.