Friday, January 22, 2016

Absence of evidence is evidence of absence

It's a well-known theorem that if conditioning on A increases the probability of B, then conditioning on not-A increases the probability of not-B. So if learning that there is evidence of B increases the probability of B, learning that there is no evidence for B increases the probability of not-B. Hence, there is a sense in which absence of evidence is evidence of absence.

Of course, the absence of evidence may be exceedingly weak evidence of absence, and that's probably the right way to take the platitude that absence of evidence isn't evidence of absence.

4 comments:

Sam Harper said...

It seems to me that absence of evidence is only evidence of absence in cases where we should expect there to be evidence if something is there. For example, if there were an elephant in the room, we should expect to see one. But if there is a spider in the room, we wouldn't necessarily expect that to be evidence since a little spider can be hard to spot.

William said...

The medical schools have terms for all this in diagnosis: see

https://www.med.emory.edu/EMAC/curriculum/diagnosis/sensand.htm

Alexander R Pruss said...

Sam:
That you don't see a spider decreases the probability that there is a giant spider there, which decreases the probability that there is a spider there.

Alexander R Pruss said...

Bibliographic addendum: The same point was made, under the same title but rather earlier, here.