chpter 1 多维数据与多元统计(多元统计分析课件-西安交通大学 严明义)

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1、CHPTER1MultivariateDataandMultivariateStatistics1.1ApplicationsofMultivariateStatisticalAnalysisMultivariatestatisticalanalysisisa“mixedbag.”Itisdifficulttoestablishaclassificationschemeformultivariatetechniquesthatbothiswidelyacceptedandindicatestheappropriatenessoft

2、hetechniques.Theobjectivesofscientificinvestigationstowhichmultivariatemethodsmostnaturallylendthemselvesincludethefollowing:1.Datareductionorstructuralsimplification.Thephenomenonbeingstudiedisrepresentedassimplyaspossiblewithoutsacrificingvaluableinformation.Itishop

3、edthatthiswillmakeinterpretationeasier.2.Sortingandgrouping.Groupsof“similar”objectsorvariablesarecreated,baseduponmeasuredcharacteristics.Alternatively,rulesforclassifyingobjectsintowell-definedgroupsmayberequired.3.Investigationofthedependenceamongvariables.Thenatur

4、eoftherelationshipsamongvariablesisofinterest.Areallthevariablesmutuallyindependentorareoneormorevariablesdependentontheothers?Ifso,how?4.Prediction.Relationsbetweenvariablesmustbedeterminedforthepurposeofpredictingthevaluesofoneormorevariablesonthebasisofobservationo

5、ntheothervariables.5.Hypothesisconstructionandtesting.Specificstatisticalhypothesis,formulatedintermsoftheparametersofmultivariatepopulations,aretested.Thismaybedowntovalidateassumptionsortoreinforcepriorconvictions.Iconcludethisbriefoverviewofmultivariatedataanalysis

6、withaquotationfromF.H.C.Marriott(Theinterpretationofmultipleobservation.London:AcademicPress1974,page89).Thestatementwasmadeinadiscussionofclusteranalysis,butIfeelitisappropriateforabroaderrangeofmethods.Youshouldkeepitinmindwheneveryouattempttoreadaboutadataanalysis.

7、Itallowsonetomaintainaproperperspectiveandnotbeoverwhelmedbytheeleganceofsomeofthetheory:Iftheresultsdisagreewithinformedopinions,donotadmitasimplelogicalinterpretation,anddonotshowupclearlyinagraphicalpresentation,theyareprobablywrong.Thereisnomagicaboutnumericalmeth

8、ods,andmanywaysinwhichtheycanbreakdown.Theyareavaluableaidtotheinterpretationofdata,notsausagemachinesautomaticallytransform