# 1 Decision Analysis with Sample Information. 2 I begin here with our familiar example. States of Nature Decision Alternatives s1s2 d187 d2145 d320-9 At.

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1 Decision Analysis with Sample Information

2 I begin here with our familiar example. States of Nature Decision Alternatives s1s2 d187 d2145 d320-9 At this point we have said the P(s1) =.8 and P(s2) =.2. It may be in the interest of the decision maker to search for more information about the states of nature. Sample information would be used to potentially change our views about the probability of s1 and s2.

3 Let’s say here that the decision maker feels that searching for more information will yield 1 of 2 things: -A favorable report in that demand for condos seems high based on many individuals expressing a demand, -An unfavorable report in that the demand for condos appears low based on many individuals being asked about their future plans and the response being no demand often. On the next slide I have reproduced the basic decision tree we had for this problem before. But now we will have to consider the tree three times: once if we do the market research and the report is favorable, a second time if we do the market research and the report is unfavorable, and a third time if we do not do the market research (which we have already done).

4 8 7 14 5 20 -9 d1 d2 d3 Strong weak strong weak Strong weak

5 If the report is favorable, say P(s1|favorable report) =.94 and P(s2|favorable report) =.06, Then the expected value of each decision alternative is d1.94(8) + (.06)(7) = 7.94 d2.94(14) + (.06)(5) = 13.46 d3.94(20) + (.06)(-9) = 18.26 The best would be d3 If the report is unfavorable, say P(s1|unfavorable report) =.35 and P(s2|unfavorable report) =.65, Then the expected value of each decision alternative is d1.35(8) + (.65)(7) = 7.35 d2.35(14) + (.65)(5) = 8.15 d3.35(20) + (.65)(-9) = 1.15 The best would be d2

6 If the additional information is not collected then we are back where we started and we have P(s1) =.8 and P(s2) =.2, and the expected value of each decision alternative is d1.8(8) +.2(7) = 7.80 d2.8(14) +.2(5) = 12.20 d3.8(20) +.2(-9) = 14.20 The best would be d3. Now, if the search for additional information happens d3 is chosen if the information is favorable and d2 is chosen if the information is unfavorable. Say P(favorable info) =.77 and P(unfavorable info) =.23. Then the expected value if additional information is searched for is.77(18.26) +.23(8.15) = 15.93. Since this is higher than 14.20 (the best if no information is search for) then the market research should happen. If information is favorable do d3, else do d2.

7 In our example 14.20 was the expected value without sample information (EVwoSI), 15.93 was the expected value with sample information (EVwSI). The expected value of sample information, EVSI, =Absolute value (EVwSI – EVwoSI) =1.73 in our example.

8 Efficiency of Sample Information You may recall we said the expected value of perfect information, EVPI, was what you could expect to gain if you had perfect information. EVSI is what is actually gained. E = (EVSI/EVPI)100 is the efficiency of sample information. Here we have (1.73/3.2)100 = 54.1%. Should we stop looking for more information about the states of nature? If the efficiency is high there is not much to gain. But if the efficiency is low you may not be able to do more because you have spent all you can hope to gain.

9 Let’s do a problem. We have state of nature alternativess1s2 d1100300 d2400200 If we do the market study and we get a favorable report the expected values are d1.57(100) +.43(300) = 186 (because P(s1|favorable report)=.57) d2.57(400) +.43(200) = 314 So you would go with d2. If we do the market study and we get an unfavorable report the expected values are d1.18(100) +.82(300) = 264 (because P(s1|unfavorable report)=.18) d2.18(400) +.82(200) = 236 So you would go with d1. If we do not do the market study the expected values are d1.4(100) +.6(300) = 220 (because P(s1)=.40) d2.4(400) +.6(200) = 280 So you would go with d2.

10 The expected value of the market study is.56(314) +.44(264) = 292. (because P(favorable report)=.56) The expected value without the study was the expected value of d2 of 280. So, do the market study and if the information is favorable do d2 and if it is unfavorable do d1.

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