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redding comments on The Heuristic About Representativeness Heuristic - Less Wrong Discussion
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Just to clarify, I feel that what you're basically saying that often what is called the base-rate fallacy is actually the result of P(E|!H) being too high.
I believe this is why Bayesians usually talk not in terms of P(H|E) but instead use Bayes Factors.
Basically, to determine how strongly ufo-sightings imply ufos, don't look at P(ufos | ufo-sightings). Instead, look at P(ufos | ufo-sightings) / P(no-ufos | ufo-sightings).
This ratio is the Bayes factor.
Thank you for your feedback.
Yes, I'm aware of likelihood ratios (and they're awesome, especially for log-odds). Earlier draft of this post ended at "the correct method for answering this query involves imagining world-where-H-is-true, imagining world-where-H-is-false and comparing the frequency of E between them", but I decided against it. And well, if some process involves X and Y, then it is correct (but maybe misleading) to say that in involves just X.
My point was that "what it does resemble?" (process where you go E -> H) was fundamentally different from "how likely is that?" (process where you go H -> E). If you calculate likelihood ratio using the-degree-of-resemblance instead of actual P(E|H) you will get wrong answer.
(Or maybe thinking about likelihood ratios will force you to snap out of representativeness heuristic, but I'm far from sure about it)
I think that I misjudged the level of my audience (this post is an expansion of /r/HPMOR/ comment) and hadn't made my point (that probabilistic thinking is more correct when you go H->E instead of vice versa) visible enough. Also, I was going to blog about likelihood ratios later (in terms of H->E and !H->E) — so again, wrong audience.
I now see some ways in which my post is debacle, and maybe it makes sense to completely rewrite it. So thank you for your feedback again.