Decision Models决策树模型ppt课件

1,DecisionModels,Chapter6,2,6.1IntroductiontoDecisionAnalysis,Thefieldofdecisionanalysisprovidesaframeworkformakingimportantdecisions.Decisionanalysisallowsustoselectadecisionfromasetofpossibledecisionalternativeswhenuncertaintiesregardingthefutureexist.Thegoalistooptimizetheresultingpayoffintermsofadecisioncriterion.,3,Maximizingthedecisionmakersutilityfunctionisthemechanismusedwhenriskisfactoredintothedecisionmakingprocess.,Maximizingexpectedprofitisacommoncriterionwhenprobabilitiescanbeassessed.,6.1IntroductiontoDecisionAnalysis,4,6.2PayoffTableAnalysis,PayoffTablesPayofftableanalysiscanbeappliedwhen:Thereisafinitesetofdiscretedecisionalternatives.Theoutcomeofadecisionisafunctionofasinglefutureevent.InaPayofftable-Therowscorrespondtothepossibledecisionalternatives.Thecolumnscorrespondtothepossiblefutureevents.Events(statesofnature)aremutuallyexclusiveandcollectivelyexhaustive.Thetableentriesarethepayoffs.,5,TOMBROWNINVESTMENTDECISION,TomBrownhasinherited$1000.Hehastodecidehowtoinvestthemoneyforoneyear.Abrokerhassuggestedfivepotentialinvestments.GoldJunkBondGrowthStockCertificateofDepositStockOptionHedge,6,Thereturnoneachinvestmentdependsonthe(uncertain)marketbehaviorduringtheyear.Tomwouldbuildapayofftabletohelpmaketheinvestmentdecision,TOMBROWN,7,Selectadecisionmakingcriterion,andapplyittothepayofftable.,TOMBROWN-Solution,Constructapayofftable.,Identifytheoptimaldecision.,Evaluatethesolution.,8,ThePayoffTable,Thestatesofnaturearemutuallyexclusiveandcollectivelyexhaustive.,9,ThePayoffTable,10,Thestockoptionalternativeisdominatedbythebondalternative,250,200,150,-100,ThePayoffTable,11,6.3DecisionMakingCriteria,Classifyingdecision-makingcriteriaDecisionmakingundercertainty.Thefuturestate-of-natureisassumedknown.Decisionmakingunderrisk.Thereissomeknowledgeoftheprobabilityofthestatesofnatureoccurring.Decisionmakingunderuncertainty.Thereisnoknowledgeabouttheprobabilityofthestatesofnatureoccurring.,12,Thedecisioncriteriaarebasedonthedecisionmakersattitudetowardlife.ThecriteriaincludetheMaximinCriterion-pessimisticorconservativeapproach.MinimaxRegretCriterion-pessimisticorconservativeapproach.MaximaxCriterion-optimisticoraggressiveapproach.PrincipleofInsufficientReasoningnoinformationaboutthelikelihoodofthevariousstatesofnature.,DecisionMakingUnderUncertainty,13,DecisionMakingUnderUncertainty-TheMaximinCriterion,14,Thiscriterionisbasedontheworst-casescenario.Itfitsbothapessimisticandaconservativedecisionmakersstyles.Apessimisticdecisionmakerbelievesthattheworstpossibleresultwillalwaysoccur.Aconservativedecisionmakerwishestoensureaguaranteedminimumpossiblepayoff.,DecisionMakingUnderUncertainty-TheMaximinCriterion,15,TOMBROWN-TheMaximinCriterion,TofindanoptimaldecisionRecordtheminimumpayoffacrossallstatesofnatureforeachdecision.Identifythedecisionwiththemaximum“minimumpayoff.”,16,TheMaximinCriterion-spreadsheet,17,ToenablethespreadsheettocorrectlyidentifytheoptimalmaximindecisionincellB11,thelabelsforcellsA4throughA7arecopiedintocellsI4throughI7(notethatcolumnIinthespreadsheetishidden).,I4,TheMaximinCriterion-spreadsheet,18,DecisionMakingUnderUncertainty-TheMinimaxRegretCriterion,19,TheMinimaxRegretCriterionThiscriterionfitsbothapessimisticandaconservativedecisionmakerapproach.Thepayofftableisbasedon“lostopportunity,”or“regret.”Thedecisionmakerincursregretbyfailingtochoosethe“best”decision.,DecisionMakingUnderUncertainty-TheMinimaxRegretCriterion,20,TheMinimaxRegretCriterionTofindanoptimaldecision,foreachstateofnature:Determinethebestpayoffoveralldecisions.Calculatetheregretforeachdecisionalternativeasthedifferencebetweenitspayoffvalueandthisbestpayoffvalue.Foreachdecisionfindthemaximumregretoverallstatesofnature.Selectthedecisionalternativethathastheminimumofthese“maximumregrets.”,DecisionMakingUnderUncertainty-TheMinimaxRegretCriterion,21,TOMBROWNRegretTable,LetusbuildtheRegretTable,InvestinginStockgeneratesnoregretwhenthemarketexhibitsalargerise,22,Investingingoldgeneratesaregretof600whenthemarketexhibitsalargerise,500(-100)=600,TOMBROWNRegretTable,23,TheMinimaxRegret-spreadsheet,24,Thiscriterionisbasedonthebestpossiblescenario.Itfitsbothanoptimisticandanaggressivedecisionmaker.Anoptimisticdecisionmakerbelievesthatthebestpossibleoutcomewillalwaystakeplaceregardlessofthedecisionmade.Anaggressivedecisionmakerlooksforthedecisionwiththehighestpayoff(whenpayoffisprofit).,DecisionMakingUnderUncertainty-TheMaximaxCriterion,25,Tofindanoptimaldecision.Findthemaximumpayoffforeachdecisionalternative.Selectthedecisionalternativethathasthemaximumofthe“maximum”payoff.,DecisionMakingUnderUncertainty-TheMaximaxCriterion,26,TOMBROWN-TheMaximaxCriterion,27,Thiscriterionmightappealtoadecisionmakerwhoisneitherpessimisticnoroptimistic.Itassumesallthestatesofnatureareequallylikelytooccur.Theproceduretofindanoptimaldecision.Foreachdecisionaddallthepayoffs.Selectthedecisionwiththelargestsum(forprofits).,DecisionMakingUnderUncertainty-ThePrincipleofInsufficientReason,28,TOMBROWN-InsufficientReason,SumofPayoffsGold600DollarsBond350DollarsStock50DollarsC/D300DollarsBasedonthiscriteriontheoptimaldecisionalternativeistoinvestingold.,29,DecisionMakingUnderUncertaintySpreadsheettemplate,30,DecisionMakingUnderRisk,Theprobabilityestimatefortheoccurrenceofeachstateofnature(ifavailable)canbeincorporatedinthesearchfortheoptimaldecision.Foreachdecisioncalculateitsexpectedpayoff.,31,DecisionMakingUnderRiskTheExpectedValueCriterion,ExpectedPayoff=S(Probability)(Payoff),Foreachdecisioncalculatetheexpectedpayoffasfollows:(Thesummationiscalculatedacrossallthestatesofnature)Selectthedecisionwiththebestexpectedpayoff,32,TOMBROWN-TheExpectedValueCriterion,EV=(0.2)(250)+(0.3)(200)+(0.3)(150)+(0.1)(-100)+(0.1)(-150)=130,33,Theexpectedvaluecriterionisusefulgenerallyintwocases:Longrunplanningisappropriate,anddecisionsituationsrepeatthemselves.Thedecisionmakerisriskneutral.,Whentousetheexpectedvalueapproach,34,TheExpectedValueCriterion-spreadsheet,35,6.4ExpectedValueofPerfectInformation,Thegaininexpectedreturnobtainedfromknowingwithcertaintythefuturestateofnatureiscalled:ExpectedValueofPerfectInformation(EVPI),36,Ifitwereknownwithcertaintythattherewillbea“LargeRise”inthemarket,Largerise,.theoptimaldecisionwouldbetoinvestin.,-10025050060,Similarly,TOMBROWN-EVPI,37,ExpectedReturnwithPerfectinformation=ERPI=0.2(500)+0.3(250)+0.3(200)+0.1(300)+0.1(60)=$271ExpectedReturnwithoutadditionalinformation=ExpectedReturnoftheEVcriterion=$130EVPI=ERPI-EREV=$271-$130=$141,TOMBROWN-EVPI,38,6.5BayesianAnalysis-DecisionMakingwithImperfectInformation,BayesianStatisticsplayaroleinassessingadditionalinformationobtainedfromvarioussources.Thisadditionalinformationmayassistinrefiningoriginalprobabilityestimates,andhelpimprovedecisionmaking.,39,TOMBROWNUsingSampleInformation,Tomcanpurchaseeconometricforecastresultsfor$50.Theforecastpredicts“negative”or“positive”econometricgrowth.Statisticsregardingtheforecastare:,WhenthestockmarketshowedalargerisetheForecastpredicteda“positivegrowth”80%ofthetime.,ShouldTompurchasetheForecast?,40,Iftheexpectedgainresultingfromthedecisionsmadewiththeforecastexceeds$50,Tomshouldpurchasetheforecast.Theexpectedgain=ExpectedpayoffwithforecastEREVTofindExpectedpayoffwithforecastTomshoulddeterminewhattodowhen:Theforecastis“positivegrowth”,Theforecastis“negativegrowth”.,TOMBROWNSolutionUsingSampleInformation,41,TomneedstoknowthefollowingprobabilitiesP(Largerise|Theforecastpredicted“Positive”)P(Smallrise|Theforecastpredicted“Positive”)P(Nochange|Theforecastpredicted“Positive”)P(Smallfall|Theforecastpredicted“Positive”)P(LargeFall|Theforecastpredicted“Positive”)P(Largerise|Theforecastpredicted“Negative”)P(Smallrise|Theforecastpredicted“Negative”)P(Nochange|Theforecastpredicted“Negative”)P(Smallfall|Theforecastpredicted“Negative”)P(LargeFall)|Theforecastpredicted“Negative”),TOMBROWNSolutionUsingSampleInformation,42,BayesTheoremprovidesaproceduretocalculatetheseprobabilities,TOMBROWNSolutionBayesTheorem,43,X,=,TOMBROWNSolutionBayesTheorem,Thetabularapproachtocalculatingposteriorprobabilitiesfor“positive”economicalforecast,44,Thetabularapproachtocalculatingposteriorprobabilitiesfor“positive”economicalforecast,TOMBROWNSolutionBayesTheorem,45,TOMBROWNSolutionBayesTheorem,Probability(Forecast=positive)=.56,Thetabularapproachtocalculatingposteriorprobabilitiesfor“positive”economicalforecast,46,TOMBROWNSolutionBayesTheorem,Probability(Forecast=negative)=.44,Thetabularapproachtocalculatingposteriorprobabilitiesfor“negative”economicalforecast,47,Posterior(revised)Probabilitiesspreadsheettemplate,48,ThisistheexpectedgainfrommakingdecisionsbasedonSampleInformation.Revisetheexpectedreturnforeachdecisionusingtheposteriorprobabilitiesasfollows:,ExpectedValueofSampleInformationEVSI,49,EV(Investin.|“Positive”forecast)=.286()+.375()+.268()+.071()+0()=EV(Investin.|“Negative”forecast)=.091()+.205()+.341()+.136()+.227()=,-100,100,200,300,$84,0,GOLD,-100,100,200,300,0,GOLD,$120,TOMBROWNConditionalExpectedValues,50,Therevisedexpectedvaluesforeachdecision:PositiveforecastNegativeforecastEV(Gold|Positive)=84EV(Gold|Negative)=120EV(Bond|Positive)=180EV(Bond|Negative)=65EV(Stock|Positive)=250EV(Stock|Negative)=-37EV(C/D|Positive)=60EV(C/D|Negative)=60,TOMBROWNConditionalExpectedValues,51,Sincetheforecastisunknownbeforeitispurchased,Tomcanonlycalculatetheexpectedreturnfrompurchasingit.Expectedreturnwhenbuyingtheforecast=ERSI=P(Forecastispositive)(EV(Stock|Forecastispositive)+P(Forecastisnegative”)(EV(Gold|Forecastisnegative)=(.56)(250)+(.44)(120)=$192.5,TOMBROWNConditionalExpectedValues,52,Theexpectedgainfrombuyingtheforecastis:EVSI=ERSIEREV=192.5130=$62.5Tomshouldpurchasetheforecast.Hisexpectedgainisgreaterthantheforecastcost.Efficiency=EVSI/EVPI=63/141=0.45,ExpectedValueofSamplingInformation(EVSI),53,TOMBROWNSolutionEVSIspreadsheettemplate,54,6.6DecisionTrees,ThePayoffTableapproachisusefulforanon-sequentialorsinglestage.Manyreal-worlddecisionproblemsconsistsofasequenceofdependentdecisions.DecisionTreesareusefulinanalyzingmulti-stagedecisionprocesses.,55,ADecisionTreeisachronologicalrepresentationofthedecisionprocess.Thetreeiscomposedofnodesandbranches.,Characteristicsofadecisiontree,Abranchemanatingfromastateofnature(chance)nodecorrespondstoaparticularstateofnature,andincludestheprobabilityofthisstateofnature.,Abranchemanatingfromadecisionnodecorrespondstoadecisionalternative.Itincludesacostorbenefitvalue.,56,BILLGALLENDEVELOPMENTCOMPANY,BGDplanstodoacommercialdevelopmentonaproperty.RelevantdataAskingpriceforthepropertyis300,000dollars.Constructioncostis500,000dollars.Sellingpriceisapproximatedat950,000dollars.Varianceapplicationcosts30,000dollarsinfeesandexpensesThereisonly40%chancethatthevariancewillbeapproved.IfBGDpurchasesthepropertyandthevarianceisdenied,thepropertycanbesoldforanetreturnof260,000dollars.Athreemonthoptiononthepropertycosts20,000dollars,whichwillallowBGDtoapplyforthevariance.,57,Aconsultantcanbehiredfor5000dollars.TheconsultantwillprovideanopinionabouttheapprovaloftheapplicationP(Consultantpredictsapproval|approvalgranted)=0.70P(Consultantpredictsdenial|approvaldenied)=0.80BGDwishestodeterminetheoptimalstrategyHire/nothiretheconsultantnow,Otherdecisionsthatfollowsequentially.,BILLGALLENDEVELOPMENTCOMPANY,58,BILLGALLEN-Solution,ConstructionoftheDecisionTreeInitiallythecompanyfacesadecisionabouthiringtheconsultant.AfterthisdecisionismademoredecisionsfollowregardingApplicationforthevariance.Purchasingtheoption.Purchasingtheproperty.,59,BILLGALLEN-TheDecisionTree,60,Buylandandapplyforvariance,Purchaseoptionandapplyforvariance,BILLGALLEN-TheDecisionTree,61,Thisiswhereweareatthisstage,BILLGALLEN-TheDecisionTree,62,BILLGALLENTheDecisionTree,Letusconsiderthedecisiontohireaconsultant,Done,63,BILLGALLEN-TheDecisionTree,Build,Sell,950,000,-500,000,260,000,Sell,64,BILLGALLEN-TheDecisionTree,Build,Sell,950,000,-500,000,260,000,Sell,Theconsultantservesasasourceforadditionalinformationaboutdenialorapprovalofthevariance.,65,BILLGALLEN-TheDecisionTree,Build,Sell,950,000,-500,000,260,000,Sell,Therefore,atthispointweneedtocalculatetheposteriorprobabilitiesfortheapprovalanddenialofthevarianceapplication,66,BILLGALLEN-TheDecisionTree,Build,Sell,950,000,-500,000,260,000,Sell,-75,000,27,25,115,000,23,24,26,TherestoftheDecisionTreeisbuiltinasimilarmanner.,67,Workbackwardfromtheendofeachbranch.Atastateofnaturenode,calculatetheexpectedvalueofthenode.Atadecisionnode,thebranchthathasthehighestendingnodevaluerepresentstheoptimaldecision.,TheDecisionTreeDeterminingtheOptimalStrategy,68,27,25,23,24,26,22,58,000,0.30,0.70,Build,Sell,950,000,-500,000,260,000,Sell,With58,000asthechancenodevalue,wecontinuebackwardtoevaluatethepreviousnodes.,BILLGALLEN-TheDecisionTreeDeterminingtheOptimalStrategy,69,Predictsapproval,Hire,Donothing,BILLGALLEN-TheDecisionTreeDeterminingtheOptimalStrategy,.4,.6,$10,000,$58,000,$-5,000,$20,000,$20,000,Buyland;Applyforvariance,Predictsdenial,Denied,Build,Sell,Sellland,Donothire,$-75,000,$115,000,.7,.3,Approved,70,BILLGALLEN-TheDecisionTreeExceladd-in:TreePlan,71,BILLGALLEN-TheDecisionTreeExceladd-in:TreePlan,72,6.7DecisionMakingandUtility,IntroductionTheexpectedvaluecriterionmaynotbeappropriateifthedecisionisaone-timeopportunitywithsubstantialrisks.Decisionmakersdonotalwayschoosedecisionsbasedontheexpectedvaluecriterion.Alotterytickethasanegativenetexpectedreturn.Insurancepoliciescostmorethanthepresentvalueoftheexpectedlosstheinsurancecompanypaystocoverinsuredlosses.,73,Itisassumedthatadecisionmakercanrankdecisionsinacoherentmanner.Utilityvalues,U(V),reflectthedecisionmakersperspectiveandattitudetowardrisk.Eachpayoffisassignedautilityvalue.Higherpayoffsgetlargerutilityvalue.Theoptimaldecisionistheonethatmaximizestheexpectedutility.,TheUtilityApproach,74,Thetechniqueprovidesaninsightfullookintotheamountofriskthedecisionmakeriswillingtotake.Theconceptisbasedonthedecisionmakerspreferencetotakingasurepayoffversusparticipatinginalottery.,DeterminingUtilityValues,75,Listeverypossiblepayoffinthepayofftableinascendingorder.Assignautilityof0tothelowestvalueandavalueof1tothehighestvalue.Forallotherpossiblepayoffs(Rij)askthedecisionmakerthefollowingquestion:,DeterminingUtilityValuesIndifferenceapproachforassigningutilityvalues,76,Supposeyouaregiventheoptiontoselectoneofthefollowingtwoalternatives:Receive$Rij(oneofthepayoffvalues)forsure,PlayagameofchancewhereyoureceiveeitherThehighestpayoffof$Rmaxwithprobabilityp,orThelowestpayoffof$Rminwithprobability1-p.,DeterminingUtilityValuesIndifferenceapproachforassigningutilityvalues,77,Rmin,Whatvalueofpwouldmakeyouindifferentbetweenthetwosituations?”,DeterminingUtilityValuesIndifferenceapproachforassigningutilityvalues,Rij,Rmax,p,1-p,78,Rmin,TheanswertothisquestionistheindifferenceprobabilityforthepayoffRijandisusedastheutilityvaluesofRij.,DeterminingUtilityValuesIndifferenceapproachforassigningutilityvalues,Rij,Rmax,p,1-p,79,DeterminingUtilityValuesIndifferenceapproachforassigningutilityvalues,Alternative1Asureevent,Alternative2(Game-of-chance),$100,$150,-50,p,1-p,Forp=1.0,youllpreferAlternative2.Forp=0.0,youllpreferAlternative1.Thus,forsomepbetween0.0and1.0youllbeindifferentbetweenthealternatives.,Example:,80,DeterminingUtilityValuesIndifferenceapproachforassigningutilityvalues,Alternative1Asureevent,Alternative2(Game-of-chance),$100,$150,-50,p,1-p,Letsassumetheprobabilityofindifferenceisp=.7.U(100)=.7U(150)+.3U(-50)=.7(1)+.3(0)=.7,81,TOMBROWN-DeterminingUtilityValues,DataThehighestpayoffwas$500.Lowestpayoffwas-$600.TheindifferenceprobabilitiesprovidedbyTomareTomwishestodeterminehisoptimalinvestmentDecision.,Payoff,-600,-200,-150,-100,0,60,100,150,200,250,300,500,Prob.,0,0.25,0.3,0.36,0.5,0.6,0.65,0.7,0.75,0.85,0.9,1,82,TOMBROWNOptimaldecision(utility),83,ThreetypesofDecisionMakers,RiskAverse-Prefersacertainoutcometoachanceoutcomehavingthesameexpectedvalue.RiskTaking-Prefersachanceoutcometoacertainoutcomehavingthesameexpectedvalue.RiskNeutral-Isindifferentbetweenachanceoutcomeandacertainoutcomehavingthesameexpectedvalue.,84,Payoff,Utility,TheUtilityCurveforaRiskAverseDecisionMaker,1000.5,2000.5,Theutilityofhaving$150onhand,islargerthantheexpectedutilityofagamewhoseexpectedvalueisalso$150.,U(100),U(200),85,Payoff,Utility,1000.5,2000.5,U(100),U(200),Ariskaversedecisionmakeravoidsthethrillofagame-of-chance,whoseexpectedvalueisEV,ifhecanhaveEVonhandforsure.,Furthermore,ariskaversedecisionmakeriswillingtopayapremium,tobuyhimself(herself)outofthegame-of-chance.,TheUtilityCurveforaRiskAverseDecisionMaker,86,Payoff,Utility,RiskAverseDecisionMaker,87,6.8GameTheory,Gametheorycanbeusedtodetermineoptimaldecisionsinfaceofotherdecisionmakingplayers.Alltheplayersareseekingtomaximizetheirreturn.Thepayoffisbasedontheactionstakenbyallthedecisionmakingplayers.,88,BynumberofplayersTwoplayers-ChessMultiplayerPokerBytotalreturnZeroSum-theamountwonandamountlostbyallcompetitorsareequal(Pokeramongfriends)NonzeroSum-theamountwonandtheamountlostbyallcompetitorsarenotequal(PokerInACasino)BysequenceofmovesSequential-eachplayergetsaplayinagivensequence.Simultaneous-allplayersplaysimultaneously.,ClassificationofGames,89,IGASUPERMARKET,ThetownofGoldBeachisservedbytwosupermarkets:IGAandSentry.Marketsharecanbeinfluencedbytheiradvertisingpolicies.Themanagerofeachsupermarketmustdecideweeklywhichareaofoperationstodiscountandemphasizeinthestoresnewspaperflyer.,90,DataTheweeklypercentagegaininmarketshareforIGA,asafunctionofadvertisingemphasis.AgaininmarketsharetoIGAresultsinequivalentlossforSentry,andviceversa(i.e.azerosumgame),IGASUPERMARKET,91,IGAneedstodetermineanadvertisingemphasisthatwillmaximizeitsexpectedchangeinmarketshareregardlessofSentrysaction.,92,IGASUPERMARKET-Solution,Topreventasurelossofmarketshare,bothIGAandSentryshouldselecttheweeklyemphasisrandomly.Thus,thequestionforbothstoresis:Whatproportionofthetimeeachareashouldbeemphasizedbyeachst