No. [...] I think it's more than terminology. And if Mencius can be dismissed as someone who does not really get Bayesian inference, one can surely not say the same of Cosma Shalizi, who has made the same argument somewhere on his blog. (It was a few years ago and I can't easily find a link. It might have been in a technical report or a published paper instead.) Suppose a Bayesian is trying to estimate the mean of a normal distribution from incoming data. He has a prior distribution of the mean, and each new observation updates that prior. But what if the data are not drawn from a normal distribution, but from the sum of two such distributions with well separated peaks? The Bayesian (he says) can never discover that. Instead, his estimate of the position of the single peak that he is committed to will wander up and down between the two real peaks, like the Flying Dutchman cursed never to find a port, while the posterior probability of seeing the data that he has seen plummets (on the log-odds scale) towards minus infinity. But he cannot avoid this: no evidence can let him update towards anything his prior gives zero probability to. What (he says) can save the Bayesian from this fate? Model-checking. Look at the data and see if they are actually consistent with any model in the class you are trying to fit. If not, think of a better model and fit that. Andrew Gelman says the same; there's a chapter of his book devoted to model checking. And here's a paper by both of them on Bayesian inference and philosophy of science, in which they explicitly describe model-checking as "non-Bayesian checking of Bayesian models". My impression (not being a statistician) is that their view is currently the standard one. I believe the hard-line Bayesian response to that would be that model checking should itself be a Bayesian process. (I'm distancing myself from this claim, because as a non-statistician, I don't need to have any position on this. I just want to see the position sta