Wiley (2004) Introduction to Bayesian Statistics

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1、PrefaceHowThisTextWasDevelopedThistextgrewoutofthecoursenotesforanIntroductiontoBayesianStatisticscoursethatIhavebeenteachingattheUniversityofWaikatoforthepastfewyears.MygoalindevelopingthiscoursewastointroduceBayesianmethodsattheearliestpossiblestage,andcoverasimilarrangeoftopicsasatraditionali

2、ntroductorystatisticscourse.ThereiscurrentlyanupsurgeinusingBayesianmethodsinappliedstatisticalanalysis,yettheIntroductiontoStatisticscoursemoststudentstakeisalmostalwaystaughtfromafrequentistperspective.Inmyview,thisisnotright.StudentswithareasonablemathematicsbackgroundshouldbeexposedtoBayesia

3、nmethodsfromthebeginning,becausethatisthedirectionappliedstatisticsismoving.MathematicalBackgroundRequiredBayesianstatisticsusestherulesofprobabilitytomakeinferences,sostudentsmusthavegoodalgebraicskillsforrecognizingandmanipulatingformulas.Ageneralknowledgeofcalculuswouldbeanadvantageinreadingt

4、hisbook.Inparticular,thestudentshouldunderstandthattheareaunderacurveisfoundbyintegration,andthatthelocationofamaximumoraminimumofacontinuousdifferentiablefunctionisfoundbysettingthederivativefunctionequaltozeroandsolving.Thebookisself-containedwithacalculusappendixstudentscanreferto.However,the

5、actualcalculususedisminimal.xiiixivPREFACEFeaturesoftheTextInthistextIhaveintroducedBayesianmethodsusingastepbystepdevelopmentfromconditionalprobability.InChapter4,theuniverseofanexperimentissetupwithtwodimensions,thehorizontaldimensionisobservable,andtheverticaldimensionisunobservable.Unconditi

6、onalprobabilitiesarefoundforeachpointintheuniverseusingthemultiplicationruleandthepriorprobabilitiesoftheunobservableevents.Conditionalprobabilityistheprobabilityonthatpartoftheuniversethatoccurred,thereduceduniverse.Itisfoundbydividingtheunconditionalprobabilitybytheirsumoverallthepossibleunobs

7、ervableevents.Becauseofwaytheuniverseisorganized,thissummingisdownthecolumninthereduceduniverse.Thedivisionscalesthemupsotheconditionalprobabilitiessumtoone.ThisresultknownasBayes’theoremisthekeytothiscourse.InChapter6thispa