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1、PrefaceThisbook,likemanybooks,wasborninfrustration.Wheninthefallof1994Isetouttoteachasecondcourseincomputationalstatisticstodoc-toralstudentsattheUniversityofMichigan,noneoftheexistingtextsseemedexactlyright.Ontheonehand,themanydecent,eveninspiring,booksonelementarycomputationalstatisticsstressthe
2、nutsandboltsofusingpackagedprogramsandemphasizemodelinterpretationmorethannumericalanalysis.Ontheotherhand,themanytheoreticaltextsinnu-mericalanalysisalmostentirelyneglecttheissuesofmostimportancetostatisticians.TheclosestbooktomyidealwastheclassicaltextofKennedyandGentle[2].Morethanadecadeandahal
3、fafteritspublication,thisbookstillhasmanyvaluablelessonstoteachstatisticians.However,uponreflectingontherapidevolutionofcomputationalstatistics,Idecidedthatthetimewasripeforanupdate.Thebookyouseebeforeyourepresentsabiasedselectionofthosetopicsintheoreticalnumericalanalysismostrelevanttostatistics.B
4、yintentthisbookisnotacompendiumoftriedandtrustedalgorithms,isnotacon-sumer’sguidetoexistingstatisticalsoftware,andisnotanexpositionofcomputergraphicsorexploratorydataanalysis.Myfocusonprinciplesofnumericalanalysisisintendedtoequipstudentstocrafttheirownsoftwareandtounderstandtheadvantagesanddisadv
5、antagesofdifferentnumericalmethods.Issuesofnumericalstability,accurateapproximation,computa-tionalcomplexity,andmathematicalmodelingsharethelimelightandtakeprecedenceoverphilosophicalquestionsofstatisticalinference.Accord-ingly,youmustlookelsewhereforadiscussionofthemeritsoffrequentistversusBayesia
6、ninference.Myattitudeisthatgooddatadeserveinspec-viPrefacetionfromavarietyofperspectives.Moreoftenthannot,thesedifferentperspectivesreinforceandclarifyratherthancontradictoneanother.Havingdeclaredatruceonissuesofinference,letmeaddthatIhavelittlepatiencewiththeviewthatmathematicsisirrelevanttostatis
7、tics.Whileitisdemeaningtostatisticstoviewitsimplyasabranchofmathe-matics,itisalsoridiculoustocontendthatstatisticscanprosperwithoutthecontinuedinfluxofnewmathematicalideas.Nowhereisthismoreevi-dentthanincomputatio
