Characterintroduction
ThomasBayes,Britishtheologian,mathematician,mathematicalstatisticianandphilosopher,WasborninLondon,Englandin1702,workedasapriest,andbecameamemberoftheRoyalSocietyin1742.
Bayeswasoneoftwopeople(theotherwasBlaisePascal)whohadamajorinfluenceontheearlydevelopmentofprobabilitytheoryandstatistics.
Personalcontribution
Bayesmainlystudiesprobabilitytheoryinmathematics.Hefirstappliedtheinductivereasoningmethodtothebasictheoryofprobabilitytheory,andfoundedtheBayesianstatisticaltheory,whichmadecontributionstostatisticaldecisionfunctions,statisticalinference,andstatisticalestimation.Publishedworksinthisareain1763,whichplayanimportantroleinmodernprobabilitytheoryandmathematicalstatistics.Bayes'otherbook"AnIntroductiontotheDoctrineofOpportunity"waspublishedin1758.ManytermsusedbyBayesarestillusedtoday.
Hismaincontributiontostatisticalreasoningistousetheconceptof"inverseprobability"andputitforwardasauniversalreasoningmethod.Bayes'theoremwasoriginallyatheoreminprobabilitytheory.Thistheoremcanbeexpressedbyamathematicalformula,whichisthefamousBayesformula.
In1763,RichardPricecompiledandpublishedBayesianresults"AnEssaytowardssolvingaProblemintheDoctrineofChances",andproposedtheBayesianformula.
AssumingthatB1,B2,...areseveralpossiblepremisesofacertainprocess,thenP(Bi)ispeople’spriorestimateofthelikelihoodofeachpremise,whichiscalledthepre-probability;IfthisprocessyieldsaresultA,thentheBayesianformulaprovidesawayforustomakeanewevaluationofthepreconditionsbasedontheappearanceofA;P(Bi∣A)isbothanewunderstandingoftheprobabilityofappearanceofthepreconditionBi,calledP(Bi∣A)istheposteriorprobability.Afteryearsofdevelopmentandimprovement,theBayesianformulaandthewholesetoftheoriesandmethodsdevelopedtherefromhavebecomeaprobabilisticandstatisticalmethodnamed"Bayes".Schoolofthoughtiswidelyusedinmanyfieldsofnaturalscienceandnationaleconomy.