HW7_Soln

# HW7_Soln - MS&E 252 Decision Analysis I Handout #23...

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MS&E 252 Handout #23 Decision Analysis I 12/7/2007 Page 1 of 23 HW#7 Solutions Homework Assignment #7- Solutions Distinctions These distinctions were prepared by the teaching team and reflect our best belief of the meanings of these terms. s A decision diagram shows the structure of a decision situation: the decisions, uncertainties and values involved as well as the relations between them. We represent these relations with arrows. An arrow from node A to node B shows that we wish to condition B on A. This leads to several different “types” of arrows, depending on the nodes which they connect. s Relevance arrows , indicating the conditioning of one uncertainty on another, show the possibility of relevance between the two uncertainties. s Informational arrows , indicating the conditioning of a decision on an uncertainty, show that we know the outcome of the uncertainty before we make the decision. s Functional arrows indicate the conditioning of a deterministic node on other nodes. The deterministic node is a function of the nodes pointing to it. s Influence arrows , indicating the conditioning of an uncertainty on a decision, show that the probabilities we assign to the uncertainty may change depending on the alternative we choose. Probabilistic questions 1) Solution: c Only statements I. and III. are true. If the results of a test cannot be observed, it is useless, since it is the observation of the test results which would allows us to update our beliefs about the distinction of interest and (perhaps) make a different decision. A test may be relevant but not material, but it must be relevant if it is to be material or economic. 2) Solution: b Begin by determining the posterior probabilities for the three detectors. This is illustrated in the trees that follow:

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MS&E 252 Handout #23 Decision Analysis I 12/7/2007 Page 2 of 23 HW#7 Solutions Assessed form, Rain Detector A Joint Inferential form, Rain Detector A Joint 0.85 "S" 0.79 S 0.34 0.34 0.4 S 0.43 "S" 0.15 "R" 0.21 R 0.06 0.09 0.15 "S" 0.11 S 0.09 0.06 0.6 R 0.57 "R" 0.85 "R" 0.89 R 0.51 0.51 Assessed form, Rain Detector B Joint Inferential form, Rain Detector B Joint 0.55 "S" 0.45 S 0.22 0.22 0.4 S 0.49 "S" 0.45 "R" 0.55 R 0.18 0.27 0.45 "S" 0.35 S 0.27 0.18 0.6 R 0.51 "R" 0.55 "R" 0.65 R 0.33 0.33 Assessed form, Rain Detector C Joint Inferential form, Rain Detector C Joint 0.3 "S" 0.22 S 0.12 0.12 0.4 S 0.54 "S" 0.7 "R" 0.78 R 0.28 0.42 0.7 "S" 0.61 S 0.42 0.28 0.6 R 0.46 "R" 0.3 "R" 0.39 R 0.18 0.18 Next, plug in the pre-posterior and posterior values into Kim’s party problem. We show the case of Detector C as an example. Note that the cost of the detector is not yet included in the analysis.
MS&E 252 Handout #23 Decision Analysis I 12/7/2007 Page 3 of 23 HW#7 Solutions Kim's party problem with Detector C Value Measure U-Value 0.22 S 100 1 O 13.1517 0.22222 0.78 R 0 0 0.22 S 90 0.95043388 0.54 "S" P 47.6549 0.64464 30.7133 0.46232 0.78 R 20 0.32285562 0.22 S 40 0.56753443 >>> I 47.6549 0.64464

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## This note was uploaded on 06/16/2010 for the course MS&E 252 taught by Professor Howard during the Fall '08 term at Stanford.

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HW7_Soln - MS&E 252 Decision Analysis I Handout #23...

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