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LESSON 7 NEW INFORMATION AND JUDGEMENT

BBA312 – Decision Analysis

DIEGO NAVARRA, DR. diego.navarra@euruni.edu

Bayes’ Theorem

Prior Probability

New Information

Posterior Probability

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

The components problem

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

Applying Bayes’ theorem to the components problem

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

(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: diego.navarra@euruni.edu

Steps to applying Bayes’ theorem

Vague priors & very reliable information

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

The effect of the reliability of information on the modification of prior probabilities

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

Applying Bayes’ theorem to a decision problem

The retailer’s problem with prior probabilities

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

Applying Bayes’ theorem to the retailer’s problem

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

Applying posterior probabilities to the retailer’s problem

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

• 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: diego.navarra@euruni.edu

Assessing the value of new information

Determining the EVPI

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

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: diego.navarra@euruni.edu

Deciding whether to buy imperfect information

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

If test indicates virus is present

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

If test indicates virus is absent

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

Determining the EVII

BBA312 – Decision Analysis (Lesson 7) Dr Diego Navarra: diego.navarra@euruni.edu

(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: diego.navarra@euruni.edu

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