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aspera comments on Bayesianism for Humans - Less Wrong

52 Post author: ChrisHallquist 29 October 2013 11:54PM

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Comment author: aspera 29 October 2013 03:58:56PM 0 points [-]

I agree that the statement is not crystal clear. It makes it possible to confuse the (change in the average) with the (average of the change).

Mathematically speaking, we represent our beliefs as a probability distribution on the possible outcomes, and change it upon seeing the result of a test (possibly for every outcome). The statement is that “if we average the possible posterior probability distributions weighted by how likely they are, we will end up with our original probability distribution.”

If that were not the case, it would imply that we were failing to make use of all of the prior information we have in our original distribution.

A misunderstood reading of the statement is that “the average of the absolute change in the probability distribution on measurement is zero.” This is not the case, as you rightly point out. It would imply that we expect the test to yield no information.