decision analysis
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Lesson7.pdf
LESSON 7 NEW INFORMATION AND JUDGEMENT
BBA312 – Decision Analysis
DIEGO NAVARRA, DR. [email protected]
Bayes’ Theorem
Prior Probability
New Information
Posterior Probability
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
Applying Bayes’ theorem to the components problem
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
(1) Construct a tree with branches representing all the possible events (2) Extend the tree by attaching to each branch a new branch which
represents the new information (3) Obtain the joint probabilities by multiplying each prior probability by the
conditional probability which follows it on the tree. (4) Sum the joint probabilities. (5) Divide the ‘appropriate’ joint probability by the sum of the joint
probabilities to obtain the required posterior probability
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
Steps to applying Bayes’ theorem
Vague priors & very reliable information
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
The effect of the reliability of information on the modification of prior probabilities
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
Applying Bayes’ theorem to a decision problem
The retailer’s problem with prior probabilities
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
Applying Bayes’ theorem to the retailer’s problem
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
Applying posterior probabilities to the retailer’s problem
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
• New information can remove or reduce the uncertainty involved in a decision
• In many circumstances it may be expensive to obtain information • Perfect reliability of information • Imperfect reliability of information
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
Assessing the value of new information
Calculating the EVPI
Test indication Prob. Best course of action
Pay off ($) Prov. x payoff ($)
Virus is present 0.7 Plant potatoes 90,000 63,000
Virus is absent 0.3 Plant alternative 30,000 9,000
Expected payoff with perfect information 72,000
Expected payoff without perfect information 57,000
Expected value of perfect information (EVPI) 15,000
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
Deciding whether to buy imperfect information
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
If test indicates virus is present
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
If test indicates virus is absent
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
(1) Determine the course of action (2) Identify the possible indications which the new information can give. (3) For each indication:
(a)Determine the probability that this indication will occur. (b)Use Bayes’ theorem to revise the probabilities (c)Determine the best course of action in the light of this indication
(4) Multiply the probability of each indication occurring by the expected payoff of the course of action (5) The expected value of the imperfect information is equal to the expected payoff with imperfect information (derived in stage 4) less the expected payoff of the course of action which would be selected using the prior probabilities (derived in stage 1).
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
Summary of the main stages in the above analysis
• Handbook of Decision Analysis, by Gregory S. Parnell, Terry Bresnick, Steven N. Tani, and Eric R. Johnson (2013); Publisher John Wiley & Sons, Chapter 8
• Decision Analysis for Management Judgment, 4th ed., Goodwin & Wright, Chapter 9
Recommended reading
BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: [email protected]
