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StatisticalRethinkingABayesianCoursewithExamplesinRandStan2
Theriseofprobabilitytheorychangedthat.StatisticalinferencecompelsusinsteadtorelyonFortunaasaservantofMinerva,tousechanceanduncertaintytodiscoverreliableknowledge.Allflavorsofstatisticalinferencehavethismotivation.ButBayesiandataanalysisembracesitmostfully,byusingthelanguageofchancetodescribetheplausibilityofdifferentpossibilities.Therearemanywaystousetheterm“Bayesian.”Butmainlyitdenotesaparticularinterpretationofprobability.Inmodestterms,Bayesianinferenceisnomorethancountingthenumbersofwaysthingscanhappen,accordingtoourassumptions.Thingsthatcanhappenmorewaysaremoreplausible.Andsinceprobabilitytheoryisjustacalculusforcounting,thismeansthatwecanuseprobabilitytheoryasageneralwaytorepresentplausibility,whetherinreferencetocountableeventsintheworldorrathertheoreticalconstructslikeparameters.Onceyouacceptthisgambit,therestfollowslogically.Oncewehavedefinedourassumptions,Bayesianinferenceforcesapurelylogicalwayofprocessingthatinformationtoproduceinference.
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