Product partition models for normal means

I consider probability models for the estimation of normal means that allow for some of the means to be equal. These probability models, called product partition models, specify prior probabilities for a random partition. The posterior probability of the partition given the observations has the same form. The resulting estimate of the means-the product estimate-is obtained by conditioning on the partition and summing over all possible partitions. The large number of computations involved leads to the use of Markov sampling to compute the product estimate. I compare the product estimate to other estimates of normal means both in a simulation study and in the prediction of baseball batting averages.