系统工程第四章.ppt

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2025-02-08 发布于上海
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系统工程第四章.ppt

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SolutionofProbabilityanalysis:

TheMaximumLikelihoodCriterionMaximumlikelihoodcriterion:Identifythemostlikelystateofnature(theonewiththelargestpriorprobability).Forthisstateofnature,findtheactionwiththemaximumpayoff.Choosethisaction.Theappealofthiscriterionisthatthemostimportantstateofnatureisthemostlikelyone,sotheactionchosenisthebestoneforthisparticularlyimportantstateofnature.Basingthedecisionontheassumptionthatthisstateofnaturewilloccurtendstogiveabetterchanceofafavorableoutcomethanassuminganyotherstateofnature.Furthermore,thecriteriondoesnotrelyonquestionablesubjectiveestimatesoftheprobabilitiesoftherespectivestatesofnatureotherthanidentifyingthemostlikelystate.Themajordrawbackofthecriterionisthatitcompletelyignoresmuchrelevantinformation.1Nostateofnatureisconsideredotherthanthemostlikelyone.2Inaproblemwithmanypossiblestatesofnature,theprobabilityofthemostlikelyonemaybequitesmall,sofocusingonjustthisonestateofnatureisquiteunwarranted.3Ineffect,thecriteriondoesnotpermitgamblingonalow-probabilitybigpayoff,nomatterhowattractivethegamblemaybe.4StateofNatureMaximinpayoffMaximuxlikelihoodAlternativeOilDry1.DrillforOil700-100-1002.SelltheLand909090900.250.75900.75Action:SelltheLandSolutionofProbabilityanalysis:BayesDecisionRulerBayesdecisionrule:Usingthebestavailableestimatesoftheprobabilitiesoftherespectivestatesofnature(currentlythepriorprobabilities),calculatetheexpectedvalueofthepayoffforeachofthepossibleactions.Choosetheactionwiththemaximumexpectedpayoff.Fortheprototypeexample,theseexpectedpayoffsarecalculatedasfollows:E[Payoff(drill)]=0.25(700)+0.75(-100)=100.E[Payoff(sell)]=0.25(90)+0.75(90)=90.Since100islargerthan90,thealte