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) 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 Estimating Revised Probabilities – Example 1 Prior Probabilities Revised Probabilities 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 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 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 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 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 Estimating Revised Probabilities Using a probability tree Refer to notes in class Refresh Bayes Rule from ADM 2303 Refer to examples in textbook Estimating Revised Probabilities – Example 1  #### You've reached the end of your free preview.

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