cscheffler

There are prior probabilities P(A) that event A occurs and P(B) that event B occurs. We want to express the statement "C provides more evidence for B than it does for A".

Your intuition before was

    P(B|C) - P(B) > P(A|C) - P(A),

aiming to express that the change in probability for B is greater than that for A, given C. The right way to do it in probability land, which lives on [0,1] is to use ratios instead of differences and actually to use the likelihood rather than the posterior:—

    P(C|B) > P(C|A), or P(C|B) / P(C|A) > 1.

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