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fa13-cs188-lecture-17-1PP

# 66 sun 100 rain 0 take u uaw leave umbrella

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Unformatted text preview: = take Weather W sun Forecast =bad 0.34 rain Optimal decision = take P(W|F=bad) 0.66 sun 100 rain 0 take U U(A,W) leave Umbrella W leave Umbrella = leave sun 20 take rain 70 Decisions as Outcome Trees Umbrella {b} take leav e U W | {b} W | {b} Weather U(t,s) Forecast =bad U(t,r) U(l,s) U(l,r) Ghostbusters Decision Network Bust U Ghost Loca)on Sensor (1,2) Sensor (1,3) … Sensor (2,1) Sensor (m,1) … Sensor (1,n) … Sensor (1,1) … Sensor (m,n) Demo: Ghostbusters Value of Informa)on Value of Informa)on   Idea: compute value of acquiring evidence D   Can be done directly from decision network   Example: buying oil drilling rights         Two blocks A and B, exactly one has oil, worth k You can drill in one loca)on Prior probabili)es 0.5 each, & mutually exclusive Drilling in either A or B has EU = k/2, MEU = k/2   Ques)on: what s the value of informa)on of O?               Value of knowing which of A or B has oil Value is expected gain in MEU from new info Survey may say oil in a or oil in b, prob 0.5 each If we know OilLoc, MEU is k (either way) Gain in MEU from knowing OilLoc? VPI(OilLoc) = k/2 Fair price of informa)on: k/2 O P a 1/2 b 1/2 U OilLoc U a DrillLoc O a k a b 0 b a 0 b b k VPI Example: Weather MEU with no evidence A Umbrella U MEU if forecast is bad Weather MEU if forecast is good...
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