BU275 Lecture 4 - notes from David Wheatley PDF

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notes from David Wheatley...

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Lecture IV: Analyzing Trees, Bayesian Updating

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Rolling back a tree o From right to left o At a chance node (circle), calculate expected value o At decision node (square), pick alternative with the best expected value o After all the calculation, the EV from the tree is 38.6 o So, if you buy the report, you will make $38600 o From previous class, EVPI was 28 o Expected Value of Sample Information= EV[With Report] – EV[w/o Report) o EV with no info (priors): 28 o EV with Sample info: 38.6 o EV with perfect info: 47 o Efficiency of report = EVSI/EVPI = 10.6 (38.6-28)/ 19 (47-28) = 55.8%

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The EVSI is the most we are willing to pay for the report. So, if the report cost less than 10.6k buy it. o If we receive a snowy report BUY 3 PLOWS o If we receive a mild report BUY 1 PLOW o If we do not buy a report BUY 2 PLOWS COVID testing with Bayes o Assume that 10% of people who go for a test are infected ▪ The rest have different cold or flu etc. o A certain COVID-19 test has a test sensitivity of 0.875 and a test specificity of 0.975 ▪ Test sensitivity is the “true positive rate”. Percent of people who have the disease who tested positive • In other words, given they have COVID, they tested positive • P(Positive| covid)=0.875 ▪ Test specificity is the “true negative rate”. Percent of people who do not have the disease who tested negative • In other words, given they do not have COVID, they tested negative • P(Negative| covid)=0.975 Positive Test

Positive Negative

Priors 0.1 0.9

Conditional 0.875 0.125

0.0875 0.1125...