the r book time series analysis

《the r book time series analysis》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、22BayesianStatisticsInsteadofasking‘whatdomydatashow?’,theBayesiananalystasks‘howdomydataalterourviewoftheworld?’.Itmaynotsoundlikemuch,butitisafundamentalchangeofoutlook.Theideaisthattheresultsofthenewstudyareassessedinthelightoftheexistingdata,toestablishanupdat

2、edassessmentofparametervaluesandtheiruncertainties.Therearenowtwomodelsratherthanone.Thereisamodelforwhatweknowalready:thisiscalledtheprior.Thenthereisamodelthatwefittoourdata:thisisthelikelihood.Thetwomodelscombinetogiveusanestimateoftheposterior.Weusetheposterior

3、distributiontomakestatisticalinferences.UnderitsBayesianinterpretation,probabilitymeasuresourconfidencethatsomethingistrue.Whenthenewstudyissmall,andexistingknowledgeisextensive,thenweshouldnotexpectourworktomakemuchdifferencetooverallunderstanding.Forinstance,ifwe

4、studied150subjectsandfoundthatageatdeathwasnotaffectedbytheirsmokinghabits,wewouldbeilladvisedtoconcludethatthisresulthadgreatgenerality.Thisisbecauseweknowfromstudiesofmanythousandsofsubjectsovermanydecadesthatsmokingleadstoareductionofabout14yearsinmeanageatdeat

5、h.Smallstudiescanbehighlyinformative,ofcourse,especiallywhentheyareoriginalandaddressimportantquestions.Butthelargerandbetterdesignedthenewstudy,themorethatstudyshouldbecapableofalteringourpriorknowledge,andifthestudyisbigenoughandsufficientlywellconducted,thenitco

6、uldturnpriorexpectationonitshead.ABayesiananalysisworksinthreesteps:
usingallthecurrentlyavailableinformationtocreateafullprobabilitymodel;
formingaposteriorinferencebyconditioningthefullprobabilitymodelonthenewdata;
criticizingthefitofthemodeltothedataandevaluatin

7、gthepredictionsitmakes.YoushouldreadBayesianDataAnalysisbyGelmanetal.(2004)forbackground,examplesandcomputationalmethodsoneachofthesesteps.OneofthestrengthsoftheBayesianapproachisthatitdoesnotrelyontwoofthemostpeculiaraspectsofthefrequentistapproach.Beginnersoften

8、thinkthat:
ifIrejectthenullhypothesisatthe5%level,thenthereisa5%chancethatthenullhypothesisistrue;
ifIestablisha95%confidenceintervalforthevalueofaparame