  We propose a new method for conducting Bayesian prediction that delivers
accurate predictions without correctly specifying the unknown true data
generating process. A prior is defined over a class of plausible predictive
models. After observing data, we update the prior to a posterior over these
models, via a criterion that captures a user-specified measure of predictive
accuracy. Under regularity, this update yields posterior concentration onto the
element of the predictive class that maximizes the expectation of the accuracy
measure. In a series of simulation experiments and empirical examples we find
notable gains in predictive accuracy relative to conventional likelihood-based
prediction.
