A Tutorial Introduction to Bayesian Analysis

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1、Bayes’RuleATutorialIntroductiontoBayesianAnalysisJamesVStoneTitle:Bayes’Rule:ATutorialIntroductiontoBayesianAnalysisAuthor:JamesVStonePublishedbySebtelPressAllrightsreserved.Nopartofthisbookmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,includi

2、ngphotocopying,recordingorbyanyinformationstorageandretrievalsystem,withoutwrittenpermissionfromtheauthor.FirstEdition,2013.TypesetinLATEX2".CoverDesignbyStefanBrazzo.Copyrightc2013byJamesVStoneFifthprinting.ISBN978-0-9563728-4-0Tomum.Itisremarkablethatasciencewhichbeg

3、anwiththecon-siderationofgamesofchanceshouldhavebecomethemostimportantobjectofhumanknowledge.PierreSimonLaplace,1812.ContentsPreface1.AnIntroductiontoBayes’Rule11.1.Example1:PoxyDiseases.................31.2.Example2:Forkandles...................161.3.Example3:FlippingC

4、oins................211.4.Example4:LightCraters.................251.5.ForwardandInverseProbability.............272.Bayes’RuleinPictures292.1.RandomVariables.....................292.2.TheRulesofProbability..................312.3.JointProbabilityandCoinFlips.............3

5、32.4.ProbabilityAsGeometricArea..............352.5.Bayes’RuleFromVennDiagrams.............412.6.Bayes’RuleandtheMedicalTest............433.DiscreteParameterValues473.1.JointProbabilityFunctions................483.2.PatientQuestions......................523.3.DerivingBay

6、es’Rule...................653.4.UsingBayes’Rule.....................683.5.Bayes’RuleandtheJointDistribution..........704.ContinuousParameterValues734.1.AContinuousLikelihoodFunction............734.2.ABinomialPrior......................784.3.ThePosterior.................

7、.......794.4.ARationalBasisForBias.................814.5.TheUniformPrior.....................814.6.FindingtheMAPAnalytically..............854.7.EvolutionofthePosterior.................874.8.ReferencePriors......................914.9.LossFunctions.......................9

8、25.GaussianParameterEstimation955.1.TheGaussianDistribution................955.2.EstimatingthePopulationMean..