HO17-PS2-Solutions

HO17-PS2-Solutions - MS&E 352 Handout #17 Decision...

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MS&E 352 Handout #17 Decision Analysis II February 20 th , 2009 ________________________________________________________________________ ________________________________________________________________________ 02/20/09 1 of 12 Problem Set #2 Solutions Problem Set #2 Due Thursday February 5 th
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MS&E 352 Handout #17 Decision Analysis II February 20 th , 2009 ________________________________________________________________________ ________________________________________________________________________ 02/20/09 2 of 12 Problem Set #2 Solutions Part I – Advanced Information Gathering Problem 1 – Alpha / Beta Detectors [35 points] Kim faces the Party Problem in Professor Howard's manuscript. Two salesmen approach her, one selling an Alpha Rain Detector, the other selling a Beta Rain Detector. After conferring with one another, they offer Kim the following opportunities. Kim can buy the Alpha Detector (at any time) for $10. Kim can buy the Beta Detector (at any time) for $13. Kim can buy both detectors (at the same time) for $16. Kim believes that the Alpha Detector is symmetric, and it has an accuracy of 0.8. In other words, {"S" | S, &} = {"R" | R, &} = 0.8 where "S" is the event that the test indicates sunny, S is the event that the weather is actually sunny (similarly for rain). Kim also believes that the Beta Detector is symmetric, with accuracy of 0.9, and that the two detector indications are irrelevant given the weather and her background state of information. She will buy a maximum of one indication from each detector (in other words, she will not buy two alpha detectors). Question 1: [7 points] Draw a decision diagram for Kim's detector purchase decision. Use report nodes, and draw it in assessment form (detector indications conditioned on weather). Question 2: [3 points] Redraw the decision diagram in inferential form (weather conditioned on detector indications).
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MS&E 352 Handout #17 Decision Analysis II February 20 th , 2009 ________________________________________________________________________ ________________________________________________________________________ 02/20/09 3 of 12 Problem Set #2 Solutions Answer: In assessed form: First Purchase Second Purchase Location Value First Report Second Report Alpha Indication Beta Indication Weather This diagram shows the information given to us. For example, we know {Alpha indication | Weather, &} (indication conditioned on weather), so we draw an arrow from Weather to Alpha indication showing that we condition indication on weather. The distinctions "Buy Alpha" or "Buy Beta" are not used even though they seem natural, as it is very difficult to build a diagram using these distinctions. When formulating a decision problem, sometimes the primary challenge is picking the right distinctions. When we flip the arrows (perform inference) between the indications and the weather, we
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HO17-PS2-Solutions - MS&E 352 Handout #17 Decision...

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