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komponisto comments on Open Thread: February 2010 - Less Wrong
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Bleg for assistance:
I’ve been intermittently discussing Bayes’ Theorem with the uninitiated for years, with uneven results. Typically, I’ll give the classic problem:
3,000 people in the US have Sudden Death Syndrome. I have a test that is 99% accurate; that is, it will wrong on any given person one percent of the time. Steve tests positive for SDS. What is the chance that he has it?
Afterwards, I explain the answer by comparing the false positives to the true positives. And, then I see the Bayes’ Theorem Look, which conveys to me this: "I know Mayne’s good with numbers, and I’m not, so I suppose he’s probably right. Still, this whole thing is some sort of impractical number magic." Then they nod politely and change the subject, and I save the use of Bayes’ Theorem as a means of solving disagreements for another day.
So this leads to my giving a very short presentation on the Prosecutor’s Fallacy next week. The basics of the fallacy are if you’ve got a one-in-3 million DNA match on a suspect, that doesn’t mean it’s three million-to-one that you’ve got that dude’s DNA. I need to present it to bright, interested people who will go straight to brain freeze if I display any equations at all. This isn’t frequentists-vs.-Bayesians; this is just a simple application of Bayes’ Theorem. (I suspect this will be easier to understand than the medical problem.)
I’ve read Bayesian explanations, but I’m aiming at people who are actively uninterested in learning math, and if I can get them to understand only the Prosecutor’s Fallacy, I’ll call Win. A larger understanding of the underlying structure would be a bigger win. Anyone done something like this before with success (or failure of either educational or entertainment value?)
I take it you've already looked at Eliezer's "Intuitive Explanation"?
I think it's really important to get the idea of a sliding scale of evidentiary strength across to people. (This is something that has occurred to me from some of my recent attempts to explain the Knox case to people without training in Bayesianism.) One's level of confidence that something is true varies continuously with the strength of the evidence. It's like a "score" that you're keeping, with information you hear about moving the score up and down.
The abstract structure of the prosecutor's fallacy is misjudging the prior probability. People forget that you start with a handicap -- and that handicap may be quite substantial. Thus, if a piece of evidence (like a test result) is worth, say "10 points" toward guilt, hearing about that piece of evidence doesn't necessarily make the score +10 in favor of guilt; if the handicap was, say, -7, then the score is only +3. If, say, a score of +15 is needed for conviction, the prosecution still has a long way to go.
(By the way, did you see my reply to your comment about psychological evidence?)