In many studies the experimenter has under consideration several (two or more) alternatives, and is studying them in order to determine which is the best (with regard to certain specified criteria of “goodness”). Such an experimenter does not wish basically to test hypotheses, or construct confidence intervals, or perform regression analyses (though these may be appropriate parts of his analysis); he does wish to select the best of several alternatives, and the major part of his analysis should therefore be directed towards this goal. It is precisely for this problem that ranking and selection procedures were developed. This paper presents an overview of some recent work in this field, with emphasis on aspects important to experimenters confronted with selection problems. Fixed sample size and sequential procedures for both the indifference zone and subset formulations of the selection problem are discussed.
Bayesian ranking and selection methods using hierarchical mixture models in microarray studies
