See, after locating the hypothesis, we can run some simple statistical checks on the hypothesis and the data to see if our prior was wrong. For example, plot the data as a histogram, and plot the hypothesis as another histogram, and if there's a lot of data and the two histograms are wildly different, we know almost for certain that the prior was wrong. As a responsible scientist, I'd do this kind of check. The catch is, a perfect Bayesian wouldn't. The question is, why?

Model checking is completely compatible with "perfect Bayesianism." In the practice of Bayesian statistics, how often is the prior distribution you use exactly the same as your actual prior distribution? The answer is never. Really, do you think your actual prior follows a gamma distribution exactly? The prior distribution you use in the computation is a model of your actual prior distribution. It's a map of your current map. With this in mind, model checking is an extremely handy way to make sure that your model of your prior is reasonable.

However, a difference in the data and a simulation from your model doesn't necessarily mean that you have an unreasonable model of your prior. You could just have really wrong priors. So you have to think about what's going on to be sure. This does somewhat limit the role of model checking relative to what Gelman is pushing.