Rejoinder.

This article presents a response to several commentaries regarding a study which proposed computations for Bayesian p values in composite null models. In the double use of data and conditioning, Michael Evans and Hal S. Stern both discussed what constitutes double use of the data in computing a p value. They take opposite perspectives on this issue. Evans argues that the only way to avoid double use of the data is to separate the data into two independent subsets, using one subset to fit the model and the other to assess the validity of the model. Because the procedures that we recommend do not formally split the data into two parts, Evans suggests that they can be guilty double use of the data. In contrast, Stern does not feel that it is necessary to worry about double use of the data the extent that we worry, he does not feel that even the posterior predictive p value involves double use of the data. These contrasting positions perfectly highlight what we view to be the main motivation for our paper. We feel that it is very important to avoid a double use of the data, but that separating the data into two independent subsets is a too drastic solution that can lose considerable power. We consider each of these issues in turn.