maximum likelihood in concept and practice在理念和实践的最大似然

maximum likelihood in concept and practice在理念和实践的最大似然

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时间:2019-02-28

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1、MaximumLikelihoodinConceptandPractice(cribbedmostlyfromGaryKing’sUnifyingPoliticalMethodology)Tuesday,September28:TheGoalsandFoundationsofMaximumLikelihoodI.DefinitionsandNotationII.TheLinearModelinaGeneralFormIII.WhyInverseProbabilityDoesn’tWorkIV.WhytheLikelihood

2、ModelofInferenceWorksI.DefinitionsandNotationA.DevelopedbystatisticianR.A.Fisherinthe1920s,borrowedfirstbyeconomists,andfinallyimportedintopoliticalscience,maximumlikelihoodprovidesafundamentalrationaleforusingappropriateestimatorsandgivesuslotsofflexibilitytomatch

3、ourstatisticalmodelstotheprocessthatwethinkgeneratedourdata.Thereareanumberoroverarchingapproachesdesignedtounifystatisticalmethodologies,butthisisbyfarthemostfamiliartopoliticalscientists.Itrequiresyoutomakeexplicitchoicesabouthowyouthinkyourdependentvariableisdis

4、tributed(themodel’sstochasticcomponent)andwhattherelationshipisbetweenyourindependentanddependentvariables(themodel’ssystematiccomponent).Then,basedonsomebasicrulesofprobability,itteachesyouhowtowriteoutalikelihoodfunctionandfindthesetofparametersmostlikelytohavege

5、neratedobserveddata,givenyourassumedmodel.Beforewelearnthestep-by-stepprocessofgettingmaximumlikelihoodestimate,weneedtolearnabitofnotation.B.LetYibea“randomvariable.”Itisrandominthatthereisstochasticvariationinitacrossmanyexperimentsforasingleobservation,andavaria

6、bleinthatitvariesacrossobservationsinasingleexperiment.Letyibeonedrawfromtherandomvariable.Letxibeonedraw(consistingofoneormoreexplanatoryfactors)fromthesocialsystemX.C.HypothesizesomemodelMabouthowthesocialsystemproducestherandomvariable.Wecanpartitionthismodelint

7、oM,thepartofthemodelthatwewillassume,andθ,thepartofthemodelcomposedofparametersthatwewillestimate.Afully“restrictive”modelhasallofitsassumptionsspecified(itisallMandnoθ);itisthemostparsimoniousmodelandomitsallofthevariables.An“unrestrictive”modelestimateseverything

8、,isallθandnoM,andismoreinterestingbutdemandsmorefromthedata.Inhypothesistesting,wewilloftencompareafairlyunrestrictivemodeltoaslightlymorerestric

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