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On Some Bayes and Empirical Bayes Selection Procedures

In: Probability and Bayesian Statistics

Author

Listed:
  • Shanti S. Gupta

    (Purdue University, Department of Statistics)

  • TaChen Liang

    (Purdue University, Department of Statistics)

Abstract

A common problem faced by an experimenter is one of comparing several populations (processes, treatments). Suppose that there are k(≥ 2) populations π1,… ,πk and for each i, πi. is characterized by the value of a parameter of interest, say θi.. The classical approach to this problem is to test the homogeneity hypothesis H0:θ1 =… = θk. However, the classical tests of homogeneity are inadequate in the sense that they do not answer a frequently encountered experimenter’s question, namely, how to identify the “best” population or how to select the more promising (worthwhile) subset of the populations for further experimentation. These problems are known as ranking and selection problems. The formulation of ranking and selection procedures has been accomplished generally using either the indifference zone approach (see Bechhofer (1954)) or the subset selection approach (see Gupta (1956, 1965)). A discussion of their differences and various modifications that have taken place since then can be found in Gupta and Panchapakesan (1979).

Suggested Citation

  • Shanti S. Gupta & TaChen Liang, 1987. "On Some Bayes and Empirical Bayes Selection Procedures," Springer Books, in: R. Viertl (ed.), Probability and Bayesian Statistics, pages 233-246, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1885-9_24
    DOI: 10.1007/978-1-4613-1885-9_24
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