Prior Probability Definition - Investopedia

Bayes' Theorem TableofContents Expand TableofContents WhatIsPriorProbability? UnderstandingPriorProbability Bayes'Theorem FAQs BusinessLeaders MathandStatistics WhatIsPriorProbability? Priorprobability,inBayesianstatistics,istheprobabilityofaneventbeforenewdataiscollected.Thisisthebestrationalassessmentoftheprobabilityofanoutcomebasedonthecurrentknowledgebeforeanexperimentisperformed. Priorprobabilitycanbecomparedwithposteriorprobability. KeyTakeaways Apriorprobability,inBayesianstatistics,istheex-antelikelihoodofaneventoccurringbeforetakingintoconsiderationanynew(posterior)information.TheposteriorprobabilityiscalculatedbyupdatingthepriorprobabilityusingBayes'theorem.Instatisticalterms,thepriorprobabilityisthebasisforposteriorprobabilities. UnderstandingPriorProbability Thepriorprobabilityofaneventwillberevisedasnewdataorinformationbecomesavailable,toproduceamoreaccuratemeasureofapotentialoutcome.ThatrevisedprobabilitybecomestheposteriorprobabilityandiscalculatedusingBayes'theorem.Instatisticalterms,theposteriorprobabilityistheprobabilityofeventAoccurringgiventhateventBhasoccurred. Example Forexample,threeacresoflandhavethelabelsA,B,andC.Oneacrehasreservesofoilbelowitssurface,whiletheothertwodonot.ThepriorprobabilityofoilbeingfoundonacreCisonethird,or0.333.ButifadrillingtestisconductedonacreB,andtheresultsindicatethatnooilispresentatthelocation,thentheposteriorprobabilityofoilbeingfoundonacresAandCbecome0.5,aseachacrehasoneoutoftwochances. Bayes'theoremisoftenappliedtodataminingandmachinelearning. Bayes'Theorem  P ( A ∣ B )   =   P ( A ∩ B ) P ( B )   =   P ( A )   ×   P ( B ∣ A ) P ( B ) where: P ( A )   =   the prior probability of  A  occurring P ( A ∣ B ) =   the conditional probability of  A    given that  B  occurs P ( B ∣ A )   =   the conditional probability of  B      given that  A  occurs \begin{aligned}&P(A\midB)\=\\frac{P(A\capB)}{P(B)}\=\\frac{P(A)\\times\P(B\midA)}{P(B)}\\&\textbf{where:}\\&P(A)\=\\text{thepriorprobabilityof}A\text{occurring}\\&P(A\midB)=\\text{theconditionalprobabilityof}A\\&\qquad\qquad\quad\\text{giventhat}B\text{occurs}\\&P(B\midA)\=\\text{theconditionalprobabilityof}B\\&\qquad\qquad\quad\\\text{giventhat}A\text{occurs}\\&P(B)\=\\text{theprobabilityof}B\text{occurring}\end{aligned} ​P(A∣B) = P(B)P(A∩B)​ = P(B)P(A) × P(B∣A)​where:P(A) = the prior probability of A occurringP(A∣B)= the conditional probability of A  given that B occursP(B∣A) = the conditional probability of B   given that A occurs​ Ifweareinterestedintheprobabilityofaneventofwhichwehavepriorobservations;wecallthisthepriorprobability.We'lldeemthiseventA,anditsprobabilityP(A).IfthereisasecondeventthataffectsP(A),whichwe'llcalleventB,thenwewanttoknowwhattheprobabilityofAisgivenBhasoccurred.Inprobabilisticnotation,thisisP(A|B),andisknownasposteriorprobabilityorrevisedprobability.Thisisbecauseithasoccurredaftertheoriginalevent,hencethepostinposterior.ThisishowBaye’stheoremuniquelyallowsustoupdateourpreviousbeliefswithnewinformation. WhatIstheDifferenceBetweenPriorandPosteriorProbability? Priorprobabilityrepresentswhatisoriginallybelievedbeforenewevidenceisintroduced,andposteriorprobabilitytakesthisnewinformationintoaccount. HowIsBayes'TheoremUsedinFinance? Infinance,Bayes'theoremcanbeusedtoupdateapreviousbeliefoncenewinformationisobtained.Thiscanbeappliedtostockreturns,observedvolatility,andsoon.Bayes'Theoremcanalsobeusedtoratethe risk oflendingmoneytopotentialborrowersbyupdatingthelikelihoodofdefaultbasedonpastexperience. HowIsBayes'TheoremUsedinMachineLearning? BayesTheoremprovidesausefulmethodforthinkingabouttherelationshipbetweenadatasetandaprobability.Itisthereforeusefulinfittingdataandtrainingalgorithms,wheretheseareabletoupdatetheirposteriorprobabilitiesgiveneachroundoftraining. 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Provider Name Description RelatedTerms Bayes'TheoremDefinition Bayes'theoremisamathematicalformulafordeterminingconditionalprobabilityofanevent.LearnhowtocalculateBayes'theoremandseeexamples. more UnderstandingPosteriorProbability Posteriorprobabilityistherevisedprobabilityofaneventoccurringaftertakingintoconsiderationnewinformation. more ConditionalProbability Conditionalprobabilityisthelikelihoodofaneventoroutcomeoccurringbasedontheoccurrenceofsomeotherpreviouseventoroutcome. more EmpiricalProbabilityDefinition Empiricalprobabilityusesthenumberofoccurrencesofanoutcomewithinasamplesetasabasisfordeterminingtheprobabilityofthatoutcome. more Chi-Square(χ2)StatisticDefinition Achi-square(χ2)statisticisatestthatmeasureshowexpectationscomparetoactualobserveddata(ormodelresults). more WhatIsSkewnessinStatistics? Skewnessreferstodistortionorasymmetryinasymmetricalbellcurve,ornormaldistribution,inasetofdata. more PartnerLinks RelatedArticles Tools HowtoUsetheBayesianMethodofFinancialForecasting Tools HowtoCalculateaZ-Score FinancialRatios HowtoCalculatetheRequiredRateofReturn(RRR) InvestingEssentials WhattheDowMeansandHowItIsCalculated FinancialRatios AnalyzeInvestmentsQuicklyWithRatios RiskManagement LearntheCommonWaystoMeasureRiskinInvestmentManagement