Comment by George Zhang (george-zhang) on Absence of Evidence Is Evidence of Absence · 2025-01-01T19:23:26.731Z · LW · GW

The odds form of Bayes Theorem is particularly useful here

$$\frac{P(H\mid E)}{P(\neg H\mid E)}=\frac{P(E\mid H)}{P(E\mid \neg H)}\cdot \frac{P\left(H\right)}{P\left(\neg H\right)}$$

which can be intuitively understood as Posterior Odds = Likelihood Ratio × Prior Odds.

It shows us exactly how we should update our belief (prior odds -> posterior odds) based on the likelihood ratio, which is essentially "the odd of evidence appearing if the hypothesis is true vs. not true. It can be interpreted intuitively as "Evidence supports whatever makes it more likely".

In the context of this article, since "no sabotage" is more likely if there is no Fifth Column, we should have stronger belief that there is no Fifth Column because there is no sabotage.