决策理论与方法_（decision theory and method _）

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1、决策理论与方法2_（Decisiontheoryandmethod2_）ThesecondchapterissubjectiveprobabilityandpriordistributionSubjective,Probability,and,Prior,DistributionThemainreferencesinthischapterare:60,52,howgodthrowsdiceThebasicconceptof2-1Probability(probability)1.frequencyFN(A)==Na/NP(A)=FN(A)...Definiti

2、onofclassicalprobabilityThedefinitionof2.Laplaceinthetheoreticalanalysisofprobability(1812)P(A)==k/NIntheformula,KisthebasiceventnumbercontainedinA,NisthetotalnumberofbasiceventsApplicableconditions1.basiceventsLimited2.eachbasicevent,etc.3.axiomaticdefinitionEisarandomtest,andSisth

3、esamplespaceofE.ForeacheventofE,AcorrespondstoadefiniterealnumberP(A)ifitsatisfies:Nonnegative:0=P(A=1)Normative:P(S)=1Thecountableadditivityof22incompatibleevents(k=1,2Ak...(Ai)Aj=.)P(Ak)=SigmaP(Ak)TheP(A)iscalledtheprobabilitythattheeventAoccursTwo,subjectiveprobability(subjective

4、,probability,likelihood)1.whyintroducesubjectiveprobabilities?.SomenaturalstatescannotberepeatedWillitraintomorrow?How'sthenewproductgoing?Whatistherateofnationaleconomicgrowthnextyear?CanyoutakeaPhD?.ThecostoftheexperimentistooexpensiveandtoocostlyExample:ContinentalmissilehitrateA

5、nestimateoftheenemy'snextmoveinawar2.subjectiveprobabilitydefinition:ameasureofrationalbeliefApossiblemeasureofwhathappenstoaparticularevent.Theextenttowhichhebelieved(orbelieved)thepossibilityofaneventtooccur.Thisdegreeofbeliefisabelief,subjective,butbasedonexperience,knowledge,and

6、knowledgeObjectiveanalysis,reasoning,andsyntheticjudgment(Assignment)isdifferentfromsubjectiveconjecture.Example:doctoralcandidates,flipcoins,flippinsThree.ThemathematicaldefinitionofprobabilityThenonemptyelementsofOmegaOmega,omega={Omega},thatis,FisasubsetofAOmegasigmaOmegaepsilonF

7、domain(i.e.;IfAisA,F,F;IfAi=Fi=1,2,...Then,Ai,F)IfP(A)istherealvaluedsetfunctionsetonF,itsatisfiesNonnegativeP(A)=0NormativeP(omega)=1ThecountableadditivityP(A)isastraight(principalorobjective)probabilitymeasure,referredtoasprobabilityOmegaisthebasiceventAforeventsThe$threepopulatio

8、n(omega,F,P)iscalle