This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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(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 Simpson’s “Paradox”...
View
Full
Document
This note was uploaded on 10/13/2011 for the course CS 440 taught by Professor Levinson,s during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Levinson,S

Click to edit the document details