A BAYESIAN TREATMENT OF A MULTIPLE COMPARISON PROBLEM FOR BINOMIAL PROBABILITIES.
Abstract
The goal of this paper is to develop a usable procedure which will solve a practical ranking problem for the probability parameters of binomial populations. The proposed procedure follows from an essentially Bayesian approach to the multiple comparisons problem applied to the binomial model. The comparisons problem is formulated in decision theoretic terms as a multiple decision problem. The loss function is taken as the sum of the losses of the component pair-wise comparison problems which generate the multiple comparisons problem. With the additive loss assumption, which generate the multiple comparisons problem. With the additive loss assumption, compatible Bayes rules for the component problems yield a minimum risk solution to the ranking problem consequently reducing the complexity of the problem. This approach to the multiple comparisons problem allows for the utilization of any prior information on the individual binomial probabilities. The ranking of the parameters is to be based on sufficient binomial probabilities. The ranking of the parameters is to be based on sufficient statistics which are the numbers of successes in samples from each population. This procedure allows for decisions to be made on unequal sample sizes. A related sequential problem is also considered. It is shown that a Bayes sequential test is truncated. An upper bound is found on the maximum sample size that a Bayes procedure can take so that its computation is possible by backward induction. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 24, 1969
- Accession Number
- AD0700229
Entities
People
- Thomas Lester Bratcher
Organizations
- Southern Methodist University