For a Bayesian to relinquish his original hypothesis that the distribution belonged to some family, he needs both a way to notice when the data are far too unlikely to have been produced from any member of that family at all, and a way to choose a different family that will fit better. The likelihood of the data given the prior distribution over the family’s parameters is straightforwardly computable (or approximated by calculating various test statistics, when the question you’re asking is “is this family of models completely wrong?”), but the process of choosing a new model is rather more murky. The small-worlders talk about judgement, reasonableness, and plausibility, while the large-worlders can at best talk about bounded-rational approximations to the universal prior, which in practice comes down to the same thing.
Yes, that’s the chapter.
For a Bayesian to relinquish his original hypothesis that the distribution belonged to some family, he needs both a way to notice when the data are far too unlikely to have been produced from any member of that family at all, and a way to choose a different family that will fit better. The likelihood of the data given the prior distribution over the family’s parameters is straightforwardly computable (or approximated by calculating various test statistics, when the question you’re asking is “is this family of models completely wrong?”), but the process of choosing a new model is rather more murky. The small-worlders talk about judgement, reasonableness, and plausibility, while the large-worlders can at best talk about bounded-rational approximations to the universal prior, which in practice comes down to the same thing.