Week 10- Decision Analysis Revised Probabilities.pdf - Business Analytics ADM2302 D Week 10 Decision Analysis Revised Probabilities(Bayes Rule Value of

Week 10- Decision Analysis Revised Probabilities.pdf -...

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Business Analytics ADM2302 D Week 10 Decision Analysis: Revised Probabilities (Bayes Rule)
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Value of Information Uncertainty Certainty Risk Decision making with: No probabilities, must apply a decision criterion Probability of future states known Complete knowledge of future states EMV aka EP(without more info) EP(perfect info) aka EPC EVPI EP(with more info) EVSI
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Estimating Revised Probabilities – Example 1 Prior Probabilities Revised Probabilities
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Estimating Revised Probabilities Allows probability values to be revised based on new information (from a survey or test market) Prior probabilities are the probability values before new information Revised probabilities (aka posterior probabilities) are obtained by combining the prior probabilities with the new information
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Estimating Revised Probabilities Given known prior probabilities for demand: P(High) = 0.30 P(Moderate) = 0.50 P(Low) = 0.20 The marketing research firm provided the following probabilities based on its track record of survey accuracy: Here the demand is “given”, but how do we find the revised probabilities where the survey result is “given”? Survey Result Was When Actual Outcome Was Positive Negative High P(P|H) = 29/30 = 0.967 P(N|H) = 1/30 = 0.033 Moderate P(P|M) = 8/15 = 0.533 P(N|M) = 7/15 = 0.467 Low P(P|L) = 2/30 = 0.067 P(N|L) = 28/30 = 0.933
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Estimating Revised Probabilities You can use either Bayes’ theorem formula, i.e. : ) ( ) ( ) | ( ) ( ) and ( ) | ( P P H P H P P P P H P P P H P ´ = = ) ( ) | ( ) ( ) | ( ) ( ) | ( ) ( ) | ( L P L P P M P M P P H P H P P H P H P P ´ + ´ + ´ ´ = = 0.967 × 0.30 0.967 × 0.30 + 0.533 × 0.50 + 0.067 × 0.20 = 0.290 0.570 = 0.509 Or, use the table approach shown on the next slides
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Estimating Revised Probabilities Positive Survey Results Joint Prob = Prior Prob x Cond Prob Revised Prob = Joint Prob / P(Positive Survey) Actual Outcome Prior Prob Cond Prob P(+|Actual) Joint Prob Revised Prob P(Actual|+) High 0.3 0.967 0.290 0.290/0.57 = 0.509 Moderate 0.5 0.533 0.267 0.267/0.57 = 0.468 Low 0.2 0.067 0.013 0.013/0.57 = 0.023 P(Positive Survey)= 0.570
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Estimating Revised Probabilities Negative Survey Results Joint Prob = Prior Prob x Cond Prob Revised Prob = Joint Prob / P(Negative Survey) Actual Outcome Prior Prob Cond Prob P(-|Actual) Joint Prob Revised Prob P(Actual|-) High 0.3 0.033 0.010 0.010/0.43 = 0.023 Moderate 0.5 0.467 0.233 0.233/0.43 = 0.543 Low 0.2 0.933 0.187 0.187/0.43 = 0.434 P(Negative Survey)= 0.430
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Estimating Revised Probabilities Using a probability tree Refer to notes in class Refresh Bayes Rule from ADM 2303 Refer to examples in textbook
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Estimating Revised Probabilities – Example 1
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