1

CHAPTER 12: VALUE OF INFORMATION

INTRODUCTION

  • information can help us make better decisions
  • information alternatives

- consult experts

- perform math/stat analyses

- conduct surveys

- read books, journals, or articles

  • DA offers methodology to assess the value of information

Illustrative Example: Wildcat Oil Drilling Problem

Reference:

Raiffa, Howard, Decision Analysis: Introductory Lectures on Choice under Uncertainty, Addison-Wesley, Reading, Massachusetts, 1968, pp. 34-36, pp. 47-50

Part I: (pp. 34-36)

  • The drilling cost is fixed at $70k.
  • Profit data :

State / Profit ($k)
Dry / 0
Wet / 120
Soaking / 270
  • Cost to determine the seismic structure is $10k
  • Joint and marginal probabilities.

Seismic Outcome
State / No Structure / Open Structure / Closed Structure / Marginal Probability
Dry / .3 / .15 / .05 / .5
Wet / .09 / .12 / .09 / .3
Soaking / .02 / .08 / .1 / .2
Marginal probability / .41 / .35 / .24 / 1.0
  • Draw the influence diagram and decision tree.
  • What is the best strategy without the seismic test?
  • What is the optimal strategy with the seismic test?
  • What is the expected value of seismic information?

Part II. Perfect Information:

EXPECTED VALUE OF PERFECT INFORMATION, EVPI

  • perfect information is always correct
  • EVPI allows us to put an upper bound on how much we would pay for any information

Part III: (p. 47)

  • The drilling cost is uncertain.

State / Probability / Drilling Cost ($k)
Low / 0.2 / 40
Medium / 0.7 / 50
High / 0.1 / 70
  • What is the new expected value? Why might an expert have given an analyst the previous value of $70k?
  • Draw the new influence diagram and decision tree.

  • Next, we do a Rainbow Diagram on the cost of the Seismic Test
  • How do we interpret the Rainbow Diagram?
  • What is the expected value with perfect information on oil?
  • How did I change the decision tree? What changes did I have to make to the influence diagram?

EV of PI[Oil]= $65k - $40k = $25k

  • What is the expected value with perfect information on drilling cost? $40k
  • How do I modify the ID and DT?

EV of PI[Drilling Cost]=$40k - $40k = 0

  • What is the expected value with perfect information on both oil and drilling cost? $65k
  • How do I modify the ID and DT?

EV of PI[Oil & Drilling Cost]= $65k - $40k = $25k

Part IV: The first seismic test accurately discloses the true seismic structure. A less expensive test ($3k) will indicate the subsurface structure, but will be wrong part of the time. What is the EVPI of the imperfect test?

  • Here’s the probability data.

State\Test / “No Structure” / “Open Structure” / “Closed Structure”
No Structure / 0.9 / 0.1 / 0.0
Open Structure / 0.2 / 0.7 / 0.1
Closed Structure / 0.1 / 0.3 / 0.6
  • Explain the data. What type of distribution is it?
  • Draw the influence diagram and the decision tree.
  • Here’s how we enter the likelihood data:
  • Next, we do a Rainbow Diagram on the cost of the Imperfect Seismic Test
  • How do we interpret these results?

Part V. Here is another decision tree that gives the same answers for the three alternatives. This tree uses GET and PAY to assign values to each node.

  • What are the benefits of this approach?

CASE SUMMARIES

Case / Uncertainties / Expected Value ($k) / Optimal Decision Policy
I.A. Basic problem with fixed drilling cost / Oil / 20 / Drill
I.B. Problem 1A plus seismic test / Oil
Seismic Structure / 22.5 / Seismic Test: Yes
SS = None: Don't Drill
SS= Open/Closed: Drill
II. Perfect Information on Oil / Oil / 55 / Dry: Don't Drill
Wet/Soaking: Drill
III.A. Basic problem with uncertain drilling cost / Oil
Drilling Cost / 40 / Drill
III.B. Problem III.A. plus seismic test / Oil
Drilling Cost
Seismic Structure / 34.3 / SS = None: Don't Drill
SS= Open/Closed: Drill
III. C. Perfect Information on Oil / Oil
Drilling Cost
Seismic Structure / 65 / Dry: Don't Drill
Wet/Soaking: Drill
III. D. Perfect Information on Drilling Cost / Oil
Drilling Cost
Seismic Structure / 40 / Drill
III. D. Perfect Information on Oil and Drilling Cost / Oil
Drilling Cost
Seismic Structure / 65 / Dry: Don't Drill
Wet/Soaking: Drill
IV. Estimated Seismic Structure / Oil
Drilling Cost
Seismic Structure
Estimated Seismic Structure / 37 / Drill

QUESTIONS:

  1. What caused the seismic test to part of the optimal policy strategy in Problem I and not in Problem III?
  1. What is the value of sample information for the above cases?

IMPORTANT DISTINCTION

  • Expected value with and expected value of

- EV with PI[X] = Expected Value with PI on random variable X

- EV of PI[X] = Expected value of PI on random variable X compared to the EV without PI on X

- EV with SI[X] = Expected Value with SI on random variable X

- EV of SI[X] = Expected value of SI on random variable X compared to the EV without SI on X

  • Both EV of PI and EV of SI are relative to our current state of information

VALUE OF INFORMATION PRINCIPLES

  • INFORMATION HAS VALUE ONLY IF IT CHANGES THE OPTIMAL DECISION POLICY
  • YOU CAN NEVER BE WORSE OFF WITH MORE (FREE) INFORMATION; BUT, ADDITIONAL INFORMATION MAY HAVE NO VALUE.
  • THE EXPECTED VALUE OF PERFECT INFORMATION PROVIDES AN UPPER BOUND ON THE AMOUNT YOU SHOULD PAY FOR INFORMATION

CONCLUDING NOTE

  • Our final decision problem had four uncertainties

- oil

- seismic structure

- estimated seismic structure

- drilling

  • Which nodes directly impact the value node?
  • Which nodes represent information that is probabilistically dependent with the nodes that impact the value node?
  • Which nodes provide imperfect information about oil?
  • Which nodes provide imperfect information about seismic structure?
  • Value of Information should be calculated for ALL combinations of uncertain nodes.

- Not possible for very large problems