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.