Bayesianideashaverecentlybeenappliedacrosssuchdiversefieldsasphilosophy,statistics,economics,psychology,artificialintelligence,andlegaltheory.FundamentalsofBayesianEpistemologyexaminesepistemologists’useofBayesianprobabilitymathematicstorepresentdegreesofbelief.MichaelG.TitelbaumprovidesanaccessibleintroductiontothekeyconceptsandprinciplesoftheBayesianformalism,enablingthereaderbothtofollowepistemologicaldebatesandtoseebroaderimplicationsVolume1beginsbymotivatingtheuseofdegreesofbeliefinepistemology.Itthenintroduces,explains,andappliesthefivecoreBayesiannormativerules:Kolmogorov’sthreeprobabilityaxioms,theRatioFormulaforconditionaldegreesofbelief,andConditionalizationforupdatingattitudesovertime.Finally,itdiscussesfurthernormativerules(suchasthePrincipalPrinciple,orindifferenceprinciples)thathavebeenproposedtosupplementorreplacethecorefive.Volume2givesargumentsforthefivecorerulesintroducedinVolume1,thenconsiderschallengestoBayesianepistemology.ItbeginsbydetailingBayesianism’ssuccessfulapplicationstoconfirmationanddecisiontheory.ThenitdescribesthreetypesofargumentsforBayesianrules,basedonrepresentationtheorems,DutchBooks,andaccuracymeasures.Finally,ittakesonobjectionstotheBayesianapproachandalternativeformalisms,includingthestatisticalapproachesoffrequentismandlikelihoodism.
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