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Abstract:
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In this paper, we fill in an important research gap in the small area literature, namely the problem of multiple comparison. We illustrate how the Bayesian approach can be applied to develop different multiple comparison procedures. Unlike the classical methods, the Bayesian method can incorporate all sources of uncertainties, irrespective of the sample size, and can make inferences conditional on the data. However, the selection of priors for the hyperparameters is one of the important problems in Bayesian analysis. We revisit this problem in the context of multiple comparison, and develop a new class of objective priors that approximate certain well-known frequentist's solutions. This class includes the well-known superharmonic prior due to Stein. The utility of our method is illustrated through data analysis.
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