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1、StatisticalPreliminariesWereviewbrieflysomeofthebackgroundthatiscommontobothclassicalstatisticsandBayesiananalysis.MoredetailsareavailableinCasellaandBerger(1990),LehmannandCasella(1998),andBickelandDoksum(2001).ThereaderinterestedinBayesiananalysiscangodirectlytoChapter
2、2afterreadingSection1.1.1.1CommonModelsAstatistician,whohasbeengivensomedataforanalysis,beginsbyprovidingaprobabilisticmodelofthewayhisdatahavebeengenerated.Usuallythedatacanbetreatedasgeneratedbyrandomsamplingorsomeotherrandommechanism.Onceamodelischosen,thedataaretreat
3、edasarandomvec•torX=(Xi,X2,...jXn)'TheprobabilitydistributionofXisspecifiedbyf{x6)whichstandsforajointdensity(oraprobabilitymassfunction),and0isanunknownconstantoravectorofunknownconstantscalledaparameter.Theparameter0maybetheunknownmeanandvarianceofapopulationfromwhich
4、Xisarandomsample,e.g.,themeanlifeofanelectricbulbortheprobabilityofdoingsomething,videExamples1.1,1.2,and1.3below.OftenthedataXarecollectedtolearnabout0,i.e.,themodelingprecedescollectionofdata.Thesetofpossiblevaluesof^,calledtheparameterspace,isdenotedby0,whichisusually
5、ap-dimensionalEuclideanspaceIZ^orsomesubsetofit,pbeingapositiveinteger.OurusualnotationfordatavectorandparametervectorareXand6,respectively,butwemayuseXand0ifthereisnofearofconfusion.Example1.1.(normaldistribution).Xi,X2,...,X^areheightsofnadults(allmalesorallfemales)sel
6、ectedatrandomfromsomepopulation.Acommonmodelisthattheyareindependently,normallydistributedwithmean/iandvariancecr^,where—000,i.e.,with6=(/x,(j^),21StatisticalPreliminaries/w(.)^n/(..i«)=n{-^e.p(-7、tributed)7V(M,8、meelectricbulbsorelectroniccomponents,say,switches.Ifthedataarearandomsampleoflifetimesofonekindofitems
