comparing Bayesian and frequentist estimates of prediction error

I had an interesting conversation with Soledad Villar (JHU) about the difference between frequentist and Bayesian descriptions or analysis of the expected wrongness (out-of-sample prediction error) for a regression or interpolation. The different statistical philosophies lead to different kinds of operations you naturally do (frequentists naturally integrate over all possible data sets; Bayesians naturally also integrate over all possible (latent) parameter values consistent with the data). These differences in turn lead to different meanings for the eventual estimates of prediction error. I'm not sure I have it all right yet, but I'd like to figure it out and write something about all this. I'm generally a pragmatist, but statistical philosophy matters sometimes!