1 / 19

Lecture 7

Lecture 7. Expected Value of Perfect Information EVPI. Administrative. Homework 4 due Wednesday Last problem is taken from a previous midterm We ’ ll go over the grading function at the end of class. Exam 1: February 24 or Feb 26. Projects…. The Original Party Problem. 40 =.4(100)+.6(0).

dominy
Download Presentation

Lecture 7

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 7 Expected Value of Perfect Information EVPI

  2. Administrative • Homework 4 due Wednesday • Last problem is taken from a previous midterm • We’ll go over the grading function at the end of class. • Exam 1: February 24 or Feb 26. • Projects…

  3. The Original Party Problem 40=.4(100)+.6(0) S .4 100 .6 0 R O S .4 90 P 48 .6 20 48=.4(90)+.6(20) R I S .4 40 .6 50 R 46=.4(40)+.6(50) Thanks to R. Howard at Stanford for the “Party Problem”

  4. S p 100 1-p 0 R O S p 90 P 1-p 20 R I S p 40 1-p 50 R Problem Given Various Probabilities of Sun 100p 20+70p 50-10p Now our optimal choice if a function of p, the probability of Sunny

  5. 100 100 90 Porch 20+70p Expected Value of Alternative 50 40 Indoors 50-10p 20 Outdoors 100p 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 p(Sun) Indoors Porch Outdoors Original Problem: Strategy Regions Prior

  6. Outdoors 100 Porch 90 .4 “Sun” 40 Indoors .6 50 What If We Knew the Weather First? 100 .4*100 + .6*50 = 70 Outdoors “Rain” 0 Porch 20 50 Recall the original solution: Use the Porch with a payoff of 48 Indoors • Expected Value of Information (EVPI) = EV with PI - Base • = 70 – 48 = 22

  7. Value with Perfect Information Value with Perfect Information Given Various Probabilities of Sun O O 100 "S" 100 "S" p .4 50+50p 70 1-p .6 "R" 50 "R" 50 I I Original Strategy Regions: Expected Value of 100 100 Perfect Information 90 Porch 20+70p Expected Value of Alternative 50 40 Indoors 50-10p 20 Outdoors 100p p(Sun) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Expected Value of Perfect Information (EVPI) EV with PI

  8. sun 50 .7 fun .3 .4 rain 75 alternative 1 40 sun .6 .7 Choose Alternative 1 EV=57.8 bad .3 rain 100 sun 50 alternative 2 .7 .3 60 rain New Base Problem: Group Outing 57.8 Group Dynamic 53.0 Compare EVwPI calculations to this base case (EV=57.8).

  9. fun .4 50 44 alt 1 .6 40 50 bad sun .7 50 alt 2 50 fun 90 .4 75 alt 1 .3 EVPI .6 100 bad 62-57.8 = 4.2 rain 90 60 alt 2 60 Value of Knowing the Weather EV with PI = 62

  10. Knowing about the Weather You get the weather information BEFORE you make a decision as to which alternative to pick.

  11. Value of Knowing the Group Same process:

  12. Knowing about the Group • Why is EVPI of the Group = 0? • Information about the group doesn’t change the decision. • Always Alternative 1: so there is no value to getting the information.

  13. Knowing about both Group and Weather • Should order of the chance nodes matter? • No: 0.7 * 0.4 = 0.4 * 0.7 • In this case, EVPI (Group and Weather) = EVPI(Group) + EVPI(Weather), • This is NOT always true.

  14. sun 50 .9 fun .3 .4 rain 75 alternative 1 40 sun .6 .9 bad .3 rain 100 sun 48 alternative 2 .9 .3 60 rain Sensitivity Analysis • What happens to the of EVPI as the probabilities vary? • There is no “in general.” It depends… • Assume the p(sun) = 0.9 • Assume Alt 2 payoff when sunny = 48 • What is the EVPI of weather?

  15. Slight Change, Big Effect on EVPI

  16. Additivity of EVPI In this problem: the additivity of the EVPI is highly dependent on the probabilities (as well as the outcome values):

  17. Example Midterm Questions

  18. Example Midterm Questions A B B D

  19. Information and Value Information (often) has value • How much value information has depends on: • Whether we change our decisions • What we know at the outset • Prior or Initial Beliefs • The accuracy of the information • Today we talked about perfect information, we just didn’t see it yet and had average over it using our prior belief. • Next time we’ll talk about imperfect information and using Bayes theorem to update our prior beliefs

More Related