Ranking and estimation of related means in the presence of a covariate—a Bayesian approach

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1128-1136
Number of pages9
JournalJournal of the American Statistical Association
Volume87
Issue number420
DOIs
StatePublished - Jan 1 1992

Fingerprint

Posterior Probability
Bayesian Approach
Covariates
Ranking
Starch
Unbalanced Designs
Ranking and Selection
Posterior Mean
Mean deviation
Standard deviation
Monte Carlo method
Numerical integration
Slope
Unknown
Evaluation
Posterior probability
Bayesian approach
Model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "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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Ranking and estimation of related means in the presence of a covariate—a Bayesian approach. / Fong, Duncan.

In: Journal of the American Statistical Association, Vol. 87, No. 420, 01.01.1992, p. 1128-1136.

Research output: Contribution to journalArticle

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