國立成功大學 統計與資料科學學系

Abstract

Eggenberger and Pólya (1923) proposed an urn model, which is well-known as the Pólya urn
and described as follows. An urn initially contains w white and r red balls.
At each stage, one ball is drawn at random from the urn and then replaced in the urn along with
c balls of the same color, where c is a fixed positive integer. Repeat the above procedure ad
infinitum. It is known that the sequence of the proportions of white balls converges almost surely
to a beta distributed random variable with parameters w/c and r/c.
In this talk, we first give a survey of urn models. Then a generalized Pólya urn model with
multiple drawings and time-dependent reinforcements will be introduced. Later, we will recall the
problem proposed by Pemantle (1990) and then give a partial answer for Pemantle's problem.