Exchangeable urn processes. (English) Zbl 0629.60044

Hill, Bruce M.; Lane, David; Sudderth, William

Ann. Probab. 15, 1586-1592 (1987).

This paper deals with the generalized two-colour urn schemes introduced by the authors [ibid. 8, 214-226 (1980; Zbl 0429.60021)]. The main theorem establishes that if the process \(Y=(Y_ 1,Y_ 2,...)\) of \(\{\) 0,1\(\}\) random variables is an exchangeable urn process then Y is a Pólya urn scheme, a sequence of independent and identically distributed random variables or a deterministic process. Further an example is given to show that the de Finetti measure for a non-deterministic exchangeable t-colour urn scheme with \(t>2\) does not have to be Dirichlet or a point mass.

Reviewer: N.Weber

MSC:

60G09	Exchangeability for stochastic processes
62A01	Foundations and philosophical topics in statistics

Keywords:

exchangeability; Pólya urn; exchangeable urn process; de Finetti measure

Citations:

Zbl 0429.60021