Lecture 10 - Imperfect Information

# Lecture 10 - Imperfect Information - Lecture 10 DADSS...

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1 Lecture 10 Decision Analysis Subjective Probability and Imperfect Information DADSS

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2 Administrative Details Term Project Introduction Questions from last class?
3 Imperfect Information Last class, we discussed the basic model for  using Bayes’ Theorem to solve decision  problems under imperfect information We also briefly introduced the calculation for  EVII Today: Calculating EVII Multiple Experts Multiple (non-dichotomous) Forecasts Multiple Uncertainties Additivity

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4 EVII Like EVPI EV of II = EV with II – EV base Now, however, EVII is dependent on accuracy  (recall that EVPI always assumes 100% accuracy) Back to the party problem P(Sun) = 0.60 Accuracy of the forecast is 75%
5 The Basic Party Problem Outdoors Indoors Sun Rain Sun Rain 200 0 120 100 0.6 0.4 0.6 0.4 120 112 EV base = 120

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6 Conditional Probabilities 0.75 0.25 0.25 0.75 0.55 0.45 0.60 0.40 1.00 P(Sun) P("Sun") P("Rain") P(Rain) 0.45 0.15 0.10 0.30 P(S | “S”) = 0.45/0.55 = 0.82 P(R | “R”) = 0.30/0.45 = 0.67 P(S | “R”) = 0.15/0.45 = 0.33 P(R | “S”) = 0.10/0.55 = 0.18
7 The EV of II Tree Outdoors Indoors “Sun” “Rain” Sun Rain 200 0 120 100 0.55 0.45 0.18 164 106.6 EV with II = 138.2 Outdoors Indoors Sun Rain Sun Rain Sun Rain 200 0 120 100 0.82 0.67 0.33 0.18 0.82 0.67 0.33 164 116.4 66 106.6 EV of II = EV with II – EV base EV of II = 138.2 – 120.0 EV of II = 18.2 Get Forecast Decide Weather

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8 EVII and Accuracy 0 5 10 15 20 25 30 35 40 45 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Accuracy Value of Information 75% 18.2 85% 26.8
9 EVII and Accuracy Why is the previous graphic  V -shaped? Now we can answer questions such as: How much would it be worth to you to find a  forecast who was slightly more accurate – say 85%  instead of 75%? Roughly, every 1% change in accuracy has a value  of \$0.90 in this problem 75% accuracy, EVII = \$18.0 76% accuracy, EVII = \$18.9 85% accuracy, EVII = \$26.8

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10 EVII by Accuracy and P(Sun) 0% 20% 40% 60% 80% 100% 50% 70% 90% 0 5 10 15 20 25 30 35 40 Value of  Inform ation P(Sun) Accuracy
11

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## This note was uploaded on 09/20/2010 for the course SDS 88223 taught by Professor Fischbeck during the Spring '10 term at Carnegie Mellon.

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Lecture 10 - Imperfect Information - Lecture 10 DADSS...

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