Let O(X) be the odds that X happens.
O(Prediction|Clue) =
O(Prediction)*
(|Prediction=Present and Clue=Present|/|Prediction=Absent and Clue=Present)*
(|Clue=Absent|/|Clue=Present|)
Correct me if I am wrong, but it seems like rarer the clue, the more effective it is at making the prediction plausible. A rare clue that only happens together with the prediction is the best updater of the prior odds.
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