作文素材总库CreateTime.ppt

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1、InformationCollection-KeyStrategyMotivationToreduceuncertaintywhichmakesuschoose“secondbest”solutionsasinsuranceConceptInsertaninformation-gatheringstage(e.g.,atest)beforedecisionproblems,asanoptionDDecisionProblemTestDecisionProblemOperationofTestEV(aftertest)>EV(withouttest)Why?Becausewecana

2、voidbadchoicesandtakeadvantageofgoodones,inlightoftestresultsQuestion:Sincetestgenerallyhasacost,isthetestworthwhile?Whatisthevalueofinformation?Doesitexceedthecostofthetest?NewInformationRevisionofPriorProbabilitiesinDecisionProblemNewExpectedValuesinDecisionProblemValueofInformation-Essenti

3、alConceptValueofinformationisanexpectedvalueExpectedvalueaftertest“k”=pk(Dk*)Pk=probablility,aftertestk,ofanobservationwhichwillleadtoanoptimaldecision(incorporatingrevisedprobabilitiesduetoobservation)Dk*ExpectedValueofinformation=EV(aftertest)-EV(withouttest)=pk(Dk*)-pk(Ej)OijkkkTest

4、Good-ReviseprobabilityMediumPoorExpectedValueofPerfectInformation-EVPIPerfectinformationisahypotheticalconceptUse:EstablishesanupperboundonvalueofanytestConcept:Imaginea“perfect”testwhichindicatedexactlywhichEvent,Ej,willoccurBydefinition,thisisthe“best”possibleinformationTherefore,the“best”poss

5、ibledecisionscanbemadeTherefore,theEVgainoverthe“notest”EVmustbethemaximumpossible-anupperlimitonthevalueofanytest!EVPIExampleQuestion:ShouldIweararaincoat?RC-Raincoat;RC-NoRaincoatTwopossibleUncertainOutcomes(p=0.4)orNoRain(p=0.6)DCC0.40.40.60.6RRNRNR5-104-2RCRRememberthatbetterchoiceistotak

6、eraincoat,EV=0.8EVPIExample(continued)PerfecttestEVPISaysRainp=0.4TakeR/C5SaysNoRainp=0.6NoR/C4CEV(aftertest)=0.4(5)+0.6(4)=4.4EVPI=4.4-0.8=3.6ApplicationofEVPIAmajoradvantage:EVPIissimpletocalculateNotice:Priorprobabilityoftheoccurrenceoftheuncertaineventmustbeequaltotheprobabilityofobservingt

7、heassociatedperfecttestresultAsa“perfecttest”,theposteriorprobabilitiesoftheuncertaineventsareeither1ot0Optimalchoicegenerallyobvious,oncewe“know”whatwillhappenTherefore,EVPIcangenerallybewrittendirectlyNoneedtouseBayes’Theo