what s the h in h likelihood a holy grail or an achilles heel shrink globally act locally sparse

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1、What'stheHinH‐likelihood:AHolyGrailoranAchilles'Heel?*UniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:

2、9780199694587PublishedtoOxfordScholarshipOnline:January2012DOI:10.1093/acprof:oso/9780199694587.001.0001What'stheHinH‐likelihood:AHolyGrailoranAchilles'Heel?*Xiao‐LiMengDOI:10.1093/acprof:oso/9780199694587.003.0016AbstractandKeywordsH‐likelihoodreferstoalikel

3、ihoodfunctionofbothfixedparametersandrandom“unobservables,”suchasmissingdataandlatentvariables.ThemethodthentypicallyproceedsbymaximizingovertheunobservablesviaanadjustedprofileH‐likelihood,andcarriesoutaFisher‐information‐likecalculationfor(predictive)varian

4、ceestimation.Theclaimedadvantageisitsavoidanceofall“bad”elementsofBayesianprediction,namelytheneedforpriorspecificationandposteriorintegration.Thistalkattemptstoprovideanin‐depthlookintooneofthemostintriguingmysteriesofmodernstatistics:whyhavetheproponentsoft

5、heH‐likelihoodmethod(LeeandNelder,1996,2001,2005,2009)beensoconvincedofitsmeritswhenalmosteveryoneelseconsidersitinvalidasageneralmethod?Thefindingsaresomewhatintriguingthemselves.Ontheonehand,H‐likelihoodturnsouttobeBartlizableundereasilyverifiableconditions

6、onthemarginaldistributionoftheunobservables,andsuchconditionspointtoatransformationofunobservablesPage1of35What'stheHinH‐likelihood:AHolyGrailoranAchilles'Heel?*thatmakesitpossibletointerpretonepredictivedistributionoftheunobservablesfromthreeperspectives:Bay

7、esian,fiducialandfrequentist.Ontheotherhand,thehopeforsuchaHolyGrailingeneralisdiminishedbythefactthatthelogH‐likelihoodsurfacecannotgenerallybesummarizedquadraticallyduetothelackofaccumulationofinformationforunobservables,whichseemstobetheAchilles'HeeloftheH

8、‐likelihoodmethod.Keywords:Bartlizability,Bayesianinference,Fiducialinference,Latentvariables,MissingData,Predictiveinference,Predictivelikelihood,Predictivepivotalquantity,JohnNelderSumm