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In this paper, I apply the decision theory and empirical Bayesian approach toconstruct confidence intervals for selected populations when true parametersfollow a mixture prior distribution. A loss function with two tuning parameters$k_1$ and $k_2$ is coined to address the mixture prior. One specific choice of$k_2$ can lead to the procedure in Qiu and Hwang (2007); the other choice of$k_2$ provides an interval construction which controls the Bayes FCR. Both theanalytical and extensive numerical simulation studies demonstrate that the newempirical Bayesian FCR controlling approach enjoys great length reduction. Atthe end, I apply different methods to a microarray data set. It turns out thatthe average length of the new approach is only 57% of that of Qiu and Hwang'sprocedure which controls the simultaneous non-coverage probability and 66% ofthat of Benjamini and Yekutieli (2005)'s procedure which controls thefrequentist's FCR.

Decision Approach and Empirical Bayes FCR-Controlling Interval for Mixed Prior Model