I think P(E∣H) is close enough to 1 to be dropped here; the more interesting thing is P(E∣¬H) (how likely would they be to make such a convincing argument if the hypothesis is false?). We have:
P(E)=P(E∣H)P(H)+P(E∣¬H)(1−P(H))∼P(H)+P(E∣¬H)(1−P(H))
so Bayes rule becomes
P(H∣E)∼P(H)P(H)+P(E∣¬H)(1−P(H))
Edit: actually use likelihood ratios; it’s way simpler.
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I think P(E∣H) is close enough to 1 to be dropped here; the more interesting thing is P(E∣¬H) (how likely would they be to make such a convincing argument if the hypothesis is false?). We have:
P(E)=P(E∣H)P(H)+P(E∣¬H)(1−P(H))∼P(H)+P(E∣¬H)(1−P(H))
so Bayes rule becomes
P(H∣E)∼P(H)P(H)+P(E∣¬H)(1−P(H))
Edit: actually use likelihood ratios; it’s way simpler.