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.
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.