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Some old and new urn models and fixed points of distributional transformations
Probability| Speaker: | Nathan Ross, UC Berkeley |
| Location: | 3106 MSB |
| Start time: | Wed, May 15 2013, 4:10PM |
Description
Since their conception 90 years ago, Polya urn models and
generalizations have been of great interest to mathematicians,
statisticians, biologists, and more recently, computer scientists. The
basic model is that an urn contains balls of different colors and at
sequential steps a ball is randomly chosen from the urn, its color noted,
and then the contents of the urn are altered based on this color; in the
classical Polya urn the ball drawn is returned to the urn along with
another of the same color. This talk will focus on the limiting
distribution of the composition of the urn in a collection of these
models, some of which (both the limits and the models) do not appear to
have been studied previously. The limiting distributions are characterized
as unique fixed points of certain distributional transformations and are
explicitly written as products of powers of independent beta and gamma
variables. Our methods suggest some conjectures for limiting distributions
in further models and these conjectures suggest a bigger picture that we
don't yet have. Joint work with Erol Pekoz and Adrian Roellin.