CSCI 3022 Lecture Notes - Lecture 6: State Space, Headache, Prostate Cancer
9 Feb 2019
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Suppose we have 2 boxes filled with green and red balls. Paul selects a ball by first choosing one of two boxes at random. He then selects one of the balls in this box at random. We want: p(b1|r) which def. of conditional probability gives as. P(b1|r) = (cid:736) p(b1(cid:15471)r) = p(r|b1)p(b1), and the ltp gives p(r) as: The notation of using evidence (ball is red) to update out belief about an event (that paul picked from box1) is the cornerstone of bayesian reasoning. The formulas we derived in the previous example are called. Allow us to write down the probability that someone who tests positive for cancer actually has cancer which is super, duper important! False positives causes stress, headache and pain. But not diagnosing cancer until it"s too late is bad too. Ex: suppose that 1% of men over the age of 40 have prostate cancer.
