多目標lecture決策分析基本概念與方法

主講:丁晶晶11課程政策2課程結構介34

Berger:Statistical ysisand大學數(shù)學（概率和統(tǒng)計和微積分多目標決 第 第部 部經驗 層次 分第 先驗信息與先驗概 確定方分 第 第部 部經驗 層次 分第 先驗信息與先驗概 確定方分 多目標決 多目標決 多目標決 钚，94號元素，放射性元素，是核工業(yè)的重要原料，可作為核的裂變物質。按照國際原子能機構的規(guī)定，原料鈾235或钚239的純度達到92%-93%稱為級，它們達到一定量即能引起 般認為，用達到級的钚6-9千克、鈾12-16千克就可制造 。但有人認為，使用高技術，用1-3千克钚、2.5-5） 如何處理決策中的不確定性 如何表示復雜的偏好關系決策問題涉及多個目標（multipleobjectives）之前的權衡（trade-多目標決 TheFoundationsof ysisRevisited(R.A.CommitteddecisionWhatyoucan

Alternatives:options(finiteorinfinite)tobeWhatyouWhatyouRiskanduncertaintyrandomfactorsoutsidethecontrol 態(tài)decisionmaker.Eachofthesepossiblesituations態(tài)bytherandomfactorsisreferredtoasapossiblestate tativemeasureofthevaluetothedecision oftheconsequencesof

DecisionWhatcan

Whatyou 實現(xiàn)一些目不同的方案得 不不同方案 通常存在不確定性（e.g.,概率不同 對決策具有不同的意義（e.g.,效用必須要從一些備選方案中做出選擇（e.g.,期望效用理論決策分析研精確地和系統(tǒng)地研究決策的特提供有效果的方法和技術來協(xié)助解決的決策問題。這括如何識別問題、組織問題、量化問題和求解問題等多目標決 決策樹（DecisionDecisiontreesprovidesausefulofwayofvisuallydisplayingthedecisionproblemandthenorganizingthecomputationalworktoachieveadecision.Decisiontreesconsistofnodesandarcs(alsoknownasAdecisionnode,representedbyasquare,indicatesthatadecisionneedstobemadeatthatpointintheAchancenode,representedbyacircle,thatarandomeventoccursatthat多目標決 ysisvs.GameExampleYouraretryingtodeterminewhether willenteramarketornot.choosesitsentrydecisionfrom{Enter,Staychoosesitspricefrom{Low,Naturepicksdemand,D,tobeRecessionwith0.3orNormalwithprobabilityPayoffLowHigh-100,--160,-Stay0,-Payoffsto )iftheeconomyisIfthereisarecession,thepayoffofeachplayerwhooperatesinthemarketis60lowerasin NotethatalthoughwealreadyspecifiedtheprobabilitiesofNature’smoveto0.7forNormal,wealsoneedtospecifyaprobability ’smove,whichsetatprobability0.5ofLowpriceandprobabilityof0.5ofHighHigh

Stay

Low0

-TheexpectedpayoffofNewcoEnter:0.5(0.7*100+0.3*40+0.7*(-100)+0.3*(-160))=-Stayout:GameHigh

LowHigh

-100,--160,-Stay

Low

0,-Thedecision SupposeNewcohasHighprice:Conclusion:highpriceispreferredifNewconentersSupposeNewcohasstayedout:Highprice:Conclusion:highpriceispreferredifNewcon多目標決 Stayout:

Conclusion:多目標決 44多目標決 多目標決 St.Petersburg如果這個賭局可以無限期進行下去，的資源是無DanielCommentariesoftheImperialAcademyofScienceSaintPetersburgEconometrica,(1954):ExpositionofaNewTheoryontheMeasurementofRisk Logarithmicutilityfunctiony=U(x)=blog(x/a)a為初始,假設初始效用為0。utility,expected“Rationalpeoplethinksatdecreasingmarginalutility：效用的增量與已擁有VonannandMorgensternTheoryofgamesandeconomicbehaviorExpectedutilityJohnJohnIfpeopledonotbelievethatmathematicsissimple,itisonlybecausetheydonotrealizehowcomplicatedlifeisQ:Ameremachinecan’treallythink,canA:Youinsistthatthereissomethingamachinecannotdo.Ifyouwill lmepreciselywhatitisamachinecannotdo,andthenIcanalwaysmakeamachinewhichwilldojustthat!剪剪石布剪（-（1，-石（1，-（-布（-（1，-強多目標決 Riskvs.Theriskversusuncertaintydistinctionisoftenuseddistinguishbetweentheoriesdonotmakeprobabilityassignmentsusethe(subjectiveorobjective)assignmentmathematicalprobabilities)不確定性可以通過有限個未知參數(shù)來表參數(shù)的不確定性可以通過概率分布來表probabilityistherelativefrequencyoftheoccurrenceofaneventinalargesetofrepetitionsoftheexperiment(orinalargeensembleofidenticalsystems)andis,assuch,apropertyofaso-calledrandomvariableprobabilityisnotdefinedasafrequencyofoccurrencebutastheplausibilitythatapropositionistrue,giventheavailableinformation.Probabilitiesarethen—intheBayesianview—notpropertiesofrandomvariablesbuta tativeencodingofourstateofknowledgeaboutthesevariables.SubjectiveProbabilityandProbability“Whetherornotthedifference(betweensubjectiveprobabilityandobjectiveprobability)isimportantphilosophically,wedon’tfeelitshouldmakeanydifferenceoperationally…”Atriple(?,F,P)iscalledaprobabilityspaceprovided?isanyset,Fisaσ-algebraofsubsetsof?,andPisaprobabilitymeasureonF.多目標決 Anexampleofill-definedBertrand’sparadox.Takeacircleofradius2inchesintheplaneandchooseachordofthiscircleatrandom.Whatistheprobabilitythischordintersectstheconcentriccircleofradius1inch?TheprobabilityofeventAisI’mabouttotossacoin.WhatistheprobabilityofitcomingupHead?Iconsiderparkingmycaronthestreettonight.Whatistheprobabilitythatitwillbestolenovernight?Iamabouttoundergoamedicaloperation.WhatistheprobabilitythatIwillsurviveit?WhatistheprobabilityofwarintheMiddleEastthis 布ImportanceofpriorinformationAlady,whoaddsmilktohertea,claimstobeablelwhethertheteaorthemilkwaspouredintothecupfirst.Inalloftentrialsconductedtotestthis,shecorrectlydetermineswhichwaspouredfirst.Adrunkenfriendsayshecanpredictthe eofaflipofafaircoin.Intentrialsconducedtotestthis,heiscorrecteachtime.Conclusion:theclaimsareWhatabouttheplausibilityofthe多目標決 ThomasBayes:(1701–AprilEnglishAnessaytowardssolvingaprobleminthedoctrineofchances,Bayes(1763) ysis:Theapproachtostatisticswhichformallyseekstouti