Ranking and Estimation of Related Means in the Presence of a Covariate—A Bayesian Approach
作者:
DuncanK. H. Fong,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1992)
卷期:
Volume 87,
issue 420
页码: 1128-1136
ISSN:0162-1459
年代: 1992
DOI:10.1080/01621459.1992.10476269
出版商: Taylor & Francis Group
关键词: Exchangeability;Hierarchical Bayes;Monte Carlo integration with antithetic acceleration;Unbalanced design
数据来源: Taylor
摘要:
Choosing the largest of several means can be a demanding problem, especially in the presence of a covariate. A hierarchical Bayesian approach to ranking and selection, as well as estimation of related means in the presence of a covariate, is considered. For the multiple slopes model we compute, in addition to the posterior means and standard deviations of the parameters, the posterior probabilities that each mean, at a given value of the covariate, is the largest. The vector of posterior probabilities thus obtained provides an easily understandable answer to the selection problem. Although calculation of the posterior probabilities may involve four-dimensional numerical integration in the difficult unbalanced design and unknown variance case, an efficient Monte Carlo method of evaluation has been developed and is given in the article. By reanalyzing a well-known data set on the breaking strength and thickness of starch films, we illustrate how our Bayesian approach produces meaningful conclusions, some of which would perhaps be difficult to obtain otherwise. For the starch film example, we found that it took only 1.4 seconds to compute the quantities of interest using an IBM 3090–600S machine. Because the computation time is quite small, it is apparent that the Bayesian procedure can be implemented for everyday use.
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