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Unformatted text preview: Announcement HW4 on BNs due today 1 Find a data sample that justifies the following interchange with Dr. Bayes Is the patient male or female? Male then administer treatment A Is the patient male or female? Female then administer treatment A Is the patient male or female? Unknown then administer treatment B 2 How to proceed? Build an empirical model (well, hybrid in fact mostly analytic) Dr. Bayes interactions are constraints on model parameters Then, either Choose parameters to satisfy constraints and make up data to yield these parameters OR Convince ourselves of their inconsistency 3 Building a Model (for Dr. Bayes) Build! Dont just wait for an inspiration What are the random variables? (what relevant features change across individuals?) G: Gender (male / female) T: Treatment (a / b) I: Improvement (yes / no) (All Boolean) Joint has ? 8 numbers, 7 parameters 4 Joint Distribution (y / n) a b m may / man mby / mbn f fay / fan fby / fbn Three Boolean random variables: Gender m/f, Treatment a/b, Improvement y/n N patients may is the number of males who improved after treatment a divide each count by N to get estimated probabilities (sample averages) which will then sum to 1 5 Constraints on Parameters Is the patient male or female? Male [Female] then administer treatment A Meaning in the model? P(I=y  G=m, T=a) > P(I=y  G=m, T=b) P(I=y  G=f, T=a) > P(I=y  G=f, T=b) Is the patient male or female? Unknown then administer treatment B P(I=y  T=a) < P(I=y  T=b) 6 Constraints on Parameters P(I=y  G=m, T=a) > P(I=y  G=m, T=b) may / ma > mby / mb may / (may + man) > mby / (mby + mbn) P(I=y  G=f, T=a) > P(I=y  G=f, T=b) fay / (fay + fan) > fby / (fby + fbn) P(I=y  T=a) < P(I=y  T=b) ay / a < by / b Some search and arithmetic 7 Dr. Bayes Gender m/f, Treatment a/b, Improvement y/n 100 patients: 50 m 50 f 50 a 50 b P(ym,a) >? P(ym,b) P(ym,a) = 25/40 = 0.625 P(ym,b) = 5/10 = 0.5 P(yf,a) >? P(yf,b) P(yf,a) = 9/10 = 0.9 P(yf,b) = 32/40 = 0.8 P(ya) = 34/50 = 0.68 P(yb) = 37/50 = 0.74 (y / n) a b male 25/15 5/5 female 9/1 32/8 8 Simpsons Paradox...
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 Fall '08
 Levinson,S

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