komponisto comments on The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom - Less Wrong

42 13 December 2009 04:16AM

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Comment author: 02 March 2010 03:37:48PM 0 points [-]

This is entirely wrong. The evidence against G should modify both P(Knox) and P(random peer that is not G) downward.

No, it is most certainly not "entirely wrong", if it is even wrong at all.

Explanatory value is the only attractor of probability: there is nothing that can possibly raise P(Knox) except improbable facts that require explanation (where the amount of probability flow as a function of the improbability of the explanandum is governed by Bayes' Theorem).

In this case, virtually all of the improbability of the data is contained in the mere fact of Kercher's death. But that fact is entirely and adequately explained by the actions of Rudy Guede; the evidence against Guede completely obstructs -- screens off -- the probability flow toward Knox.

That is the argument made in the post. Nowhere did I say that evidence of Guede's guilt is evidence of Knox's innocence, in the sense of lowering P(Knox) to below the prior. But the evidence against Guede absolutely is evidence against the hypothesis that Knox killed Kercher without Guede -- which is most of the Knox hypothesis-space (and thus where most of the probability flow toward Knox arising from Kercher's death was concentrated)!

(This point is especially important in view of all those comments from people saying that "the prior" should (already) take into account the fact that Kercher was killed. Well, if that's your prior, then it most definitely is lowered by the evidence against Guede!)

When you make a statistical argument of the form "well, a homicide was committed, so there's some probability of multiple attackers", you're starting from a position of ignorance of the details of the case, and computing an expected probability over all the various scenarios where there exists evidence of multiple attackers. But here, we know the details of the case, and we know that there is scant evidence of anybody but Rudy Guede being guilty (at least, we do if we're capable of telling strong evidence from weak).

It's clear that the evidence against K should be overwhelmed by the evidence against G, given that no solid connection was established between G and K. But it isn't zero evidence, it is merely very weak evidence.

You have established a safety heuristic to keep yourself from overvaluing weak evidence, but your safety heuristic has it's own shortcomings, because it has caused you to give it zero weight, which is obviously wrong.

represent nothing but uncharitable pedantry -- the Bayesian analogue of my pointing out to you that "its" in the above sentence should be spelled without an apostrophe. It's not, and has never been, a question of whether P(Knox) is literally greater than P(random peer); the question is whether it's noticeably greater. If it makes you happy, I'm willing to concede that the evidence in this case raises P(Knox) from 0.001 to something like 0.0034. But that scarcely makes my argument "wrong", let alone "entirely wrong".

So that's why I have downvoted your comment: because, while it sounds all learned and serious, like you have an important probability-theoretic lesson to teach, it reduces to nothing more than a snark. (In fact, it may have been the exact comment I was thinking of when I wrote this.)

Seriously: "entirely wrong"? WTF?

Comment author: 25 March 2010 06:06:04PM 0 points [-]

since you appear to still be watching this thread, it seems worth a reply even 3 months later.

Clearly "entirely wrong" is too strong and unnecessary verbiage in any case. I admit it did not even occur to me that you were using "=" to mean only "essentially equal in absolute terms".

Note, my comment was referring only to your response to Psychohistorian, not your general argument about why P(Knox) is very small given the information presented at trial, with which I agree wholeheartedly.

I apologize for my confusion. Here and in a few other comments, you seemed to be asserting not merely that the strong evidence against G put so much probability mass into P(G) that the differences between P(Knox) and P(random peer) became much too small to care about in absolute terms, but that it somehow changed the relative dynamic between P(K) and P(rp). The fact that neither probability was worth worrying about in legal terms doesn't change the '>' vs. '=' question, and that's the only thing I was responding to there. I also suspect the distinction matters in practice in rare cases, so I saw it as important enough to be worth picking the nit.