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cousin_it comments on Open Thread June 2010, Part 4 - Less Wrong
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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.