Bayesian methodology for combining the results from different experiments when the specifications for pooling are uncertain: II

Malec and Sedransk (Biometrika 79 (1992) 593) develop a Bayesian procedure for estimation of the mean corresponding to one specified experiment among a set of seemingly similar experiments. To provide a method that is invariant to a change in the scale of measuring the variable of interest, they employ an empirical Bayes argument at a key step. In this note we provide a fully Bayesian justification for the results in Malec and Sedransk. We also note that the problem addressed here occurs in other situations.