I think this is an amazing example of Bayesian methods being more precise and harder to abuse than the tropes of Traditional Rationality. I've mentioned this concept to a few friends and they didn't quite "get it" until I took the time to explain Bayes' Theorem.
On a related and shamelessly self-promoting note, this post inspired me to re-explain the concept here.
The main edit I would make to EY's point is that we are really considering 3 hypotheses here, not just two. H1 is that a Japanese fifth column exists and is currently actively engaged in covert operations. H2 is that no fifth column exists. H3 is that a fifth column exists and is remaining low profile and organizing in preparation for covert operations. In this analysis, P(H3) < P(any fifth column exists), because it specifies an additional detail. However P(E|H3) is about equal to P(E|H2) (a secretive fifth column might generate some minor acts of sabotage, but so could a few disorganized malcontents). In that case, the observation ~E would pull probability mass away from H1 and towards H2 and H3, but H2 and H3 would not gain or lose probability mass relative to each other. In this case, the debate would then center on the question of our prior probabilities for H2 relative to H3, and P(H3|I) is almost certainly less than P(H2|I).
I agree. We discussed this point in this thread of the original post:
http://lesswrong.com/lw/ih/absence_of_evidence_is_evidence_of_absence/35ra
Let E stand for the observation of sabotage, H1 for the hypothesis of a Japanese-American Fifth Column, and H2 for the hypothesis that no Fifth Column exists. Whatever the likelihood that a Fifth Column would do no sabotage, the probability P(E|H1), it cannot be as large as the likelihood that no Fifth Column does no sabotage, the probability P(E|H2).
I feel like there is a mistake here. Shouldn't E stand for the observation of no sabotage?
Title: [SEQ RERUN] Absence of Evidence Is Evidence of Absence Tags: sequence_reruns Today's post, Absence of Evidence Is Evidence of Absence was originally published on 12 August 2007. A summary (taken from the LW wiki):
Absence of proof is not proof of absence. But absence of evidence is always evidence of absence. According to the probability calculus, if P(H|E) > P(H) (observing E would be evidence for hypothesis H), then P(H|~E) < P(H) (absence of E is evidence against H). The absence of an observation may be strong evidence or very weak evidence of absence, but it is always evidence.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was I Defy the Data!, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
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