Lect21 - Announcement • HW4 on BNs due today 1 Find a...

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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! Don’t 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(y|m,a) >? P(y|m,b) • P(y|m,a) = 25/40 = 0.625 P(y|m,b) = 5/10 = 0.5 • P(y|f,a) >? P(y|f,b) • P(y|f,a) = 9/10 = 0.9 P(y|f,b) = 32/40 = 0.8 • P(y|a) = 34/50 = 0.68 P(y|b) = 37/50 = 0.74 (y / n) a b male 25/15 5/5 female 9/1 32/8 8 Simpson’s “Paradox”...
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Lect21 - Announcement • HW4 on BNs due today 1 Find a...

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