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cousin_it comments on Inherited Improbabilities: Transferring the Burden of Proof - Less Wrong
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I'm not sure if I understand the post completely. Is the following a fair translation?
"If our prior against Knox's guilt is 1:1000000, and a staged burglary would imply with 99% certainty that Knox is guilty, and we have 1000:1 evidence that the burglary was staged, then mathematically this isn't enough to convict Knox. You need more evidence."
(For some reason the post is much longer than that, and makes all those arguments whose purpose I don't understand...)
Such as....?
Yes, the point is a mathematical triviality. For that matter, so is Bayes' theorem itself. That doesn't mean that everybody grasps its implications at once, so that it isn't worth writing detailed posts on.
Pretty much, I think.
If the prior P(guilty) is 1:1000000 and P(guilty|staged) is really high, a consistent prior requires that P(staged) is around 1:1000000 as well. Therefore 1000:1 evidence isn't enough.