JSM 2004 - Toronto

Abstract #300188

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Activity Number: 67
Type: Invited
Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #300188
Title: Contributions to Group Testing and to the Dirichlet Distribution
Author(s): Ingram Olkin*+
Companies: Stanford University
Address: Department of Statistics, Stanford, CA, 94305-4065,
Keywords:
Abstract:

The group-testing problem is the determination of a testing strategy whereby each of N individuals is to be labeled "has hepatitis" or "does not have hepatitis." The key ingredient is that the relevant blood tests can be carried out for groups of individuals. Consequently, if none of the individuals has hepatitis then there is a savings in not having to carry out multiple tests. We here describe Milton Sobel's contrinutions to the solution of this problem. The Dirichlet distribution can be viewed as a multivariate extension of the beta distribution. Just as the beta distribution represents the tail of a binomial distribution, the Dirichlet distribution represents the tail of a multinomial distribution. However, there now is a multitude of stopping procedures for different sampling protocols. Milton Sobel has been one of the leaders in the development of the theory of Dirichlet distributions, and we here provide a review of his contributions.

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