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saturn comments on Open Thread June 2010, Part 4 - Less Wrong
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This sounds like a confusion between a theoretical perfect Bayesian and practical approximations. The perfect Bayesian wouldn't have any use for model checking because from the start it always considers every hypothesis it is capable of formulating, whereas the prior used by a human scientist won't ever even come close to encoding all of their knowledge.
(A more "Bayesian" alternative to model checking is to have an explicit "none of the above" hypothesis as part of your prior.)
NOTA is addressed in the paper as inadequate. What does it predict?
See here.
I don't see how that's possible. How do you compute the likelihood of the NOTA hypothesis given the data?
NOTA is not well-specified in the general case, but in at least one specific case it's been done. Jaynes's student Larry Bretthorst made a useable NOTA hypothesis in a simplified version of a radar target identification problem (link to a pdf of the doc).
(Somewhat bizarrely, the same sort of approach could probably be made to work in certain problems in proteomics in which the data-generating process shares the key features of the data-generating process in Bretthorst's simplified problem.)
If I'm not mistaken, such problems would contain some enumerated hypotheses - point peaks in a well-defined parameter space - and the NOTA hypothesis would be a uniformly thin layer over the rest of that space. Can't tell what key features the data-generating process must have, though. Or am I failing reading comprehension again?
Yep.
I think the key features that make the NOTA hypothesis feasible are (i) all possible hypotheses generate signals of a known form (but with free parameters), and (ii) although the space of all possible hypotheses is too large to enumerate, we have a partial library of "interesting" hypotheses of particularly high prior probability for which the generated signals are known even more specifically than in the general case.