04 Date 05112013 Title Multivariate likelihood ratio calculation and evaluation Author David Lucy Maintainer David Lucy Description Functions for calculating and evaluating likelihood ratios from unimultivariate continu ous observations Imports isoto ID: 42758
Download Pdf The PPT/PDF document "Package comparison February Version" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Package`comparison'August5,2020Version1.0-5Date2020-08-04TitleMultivariateLikelihoodRatioCalculationandEvaluationEncodingUTF-8DescriptionFunctionsforcalculatingandevaluatinglikelihoodratiosfromuni/multivariatecontinu-ousobservations.Thepackageincludesthetwo-levelfunctionstocalculatetheLRassumingmultivariatenormality,andanotherwithdropsthisassumptionandusesamultivariatekerneldensityestimate.Thepackagealsocon-tainscodetoperformempiricalcrossentropy(ECE)calibrationoflikelihoodratios.TheLRfunctionsarebasedprimarilyonAitken,C.G.G.andLucy,D.(2004) oi:;.1;F/;&#xj.00;5-];&#xTJ 0;&#x -11;&#x.955;&#x Td ;&#x[000;9254.2003.05271.x, Evaluationoftraceevidenceintheformofmultivariatedata, JournaloftheRoyalStatisticalSociety:SeriesC(AppliedStatistics),53:109-122.TheECEfunctionsarebasedprimarilyonD.RamosandJ.Gonzalez-Rodrigues,(2008) Cross-entropyanalysisoftheinformationinforensicspeakerrecognition, inProc.IEEEOdyssey,SpeakerLang.Recognit.Workshop.DependsR oi:;.1;F/;&#xj.00;5-];&#xTJ 0;&#x -11;&#x.955;&#x Td ;&#x[000;(=3.5.0)ImportsisotoneLicenseGPL oi:;.1;F/;&#xj.00;5-];&#xTJ 0;&#x -11;&#x.955;&#x Td ;&#x[000;(=2)URLgithub.com/jmcurran/comparisonLazyLoadyesRoxygenNote7.1.1NeedsCompilationnoAuthorDavidLucy[aut],JamesCurran[aut,cre],AgnieszkaMartyna[aut]MaintainerJamesCurran&#xj.cu;&#xrran;&#x@auc;&#xklan; .ac;&#x.nz0;RepositoryCRANDate/Publication2020-08-0511:40:02UTC1 2calc.eceRtopicsdocumented:calc.ece...........................................2calibrate.set.........................................3comparison.........................................4glass.............................................5plot.ece...........................................6two.level.comparison.items.................................7two.level.components....................................7two.level.density.LR....................................8two.level.lindley.LR.....................................9two.level.normal.LR....................................11Index13 calc.eceEmpiricalcross-entropy(ECE)calculation DescriptionCalculatestheempiricalcross-entropy(ECE)forlikelihoodratiosfromasequencesameanddif-ferentitemcomparisons.Usagecalc.ece(LR.ss,LR.ds,prior=seq(from=0.01,to=0.99,length=99))ArgumentsLR.ssavectoroflikelihoodratios(LRs)fromsamesourcecalculationsLR.dsavectorofLRsfromdifferentsourcecalculationsprioravectorofordinatesforthepriorinascendingorder,andbetween0and1.Defaultis99divisionsof0.01to0.99.DetailsAcknowledgements:Thefunctiontocalculatethevaluesofthelikelihoodratioforthecalibrated.setdrawsheavilyupontheopt_loglr.mfunctionfromNikoBrummer'sFoCalpackageforMatlab.ValueReturnsanS3objectofclasseceAuthor(s)DavidLucy calibrate.set3References@referencesD.RamosandJ.Gonzalez-Rodrigues,(2008)"Cross-entropyanalysisoftheinforma-tioninforensicspeakerrecognition,"inProc.IEEEOdyssey,SpeakerLang.Recognit.Workshop.Zadora,G.&Ramos,D.(2010)Evaluationofglasssamplesforforensicpurposes-anapplica-tionoflikelihoodratiomodelandinformation-theoreticalapproach.ChemometricsandIntelligentLaboratory:102;63-83.SeeAlsoisotone::gpava(),calibrate.set()ExamplesLR.same=c(0.5,2,4,6,8,10)#thesamehas1LR1LR.different=c(0.2,0.4,0.6,0.8,1.1)#thedifferenthas1LR&#x-500;1ece.1=calc.ece(LR.same,LR.different)#simplestinvocationplot(ece.1)#useplotmethod calibrate.setCalculatethecalibratedsetofideaLRs DescriptionCalculatesandreturnsthecalibratedsetofideal LRsfromtheobservedLRsusingthepenalisedad-jacentviolatorsalgorithm.ThisisverymucharewriteofNicoBrummer soptloglr()`functionforMatlab.Usagecalibrate.set(LR.ss,LR.ds,method=c("raw","laplace"))ArgumentsLR.ssavectoroflikelihoodratiosforthecomparisonsofitemsknowntobefromthesamesourceLR.dsavectoroflikelihoodratiosforthecomparisonsofitemsknowntobefromdifferentsourcesmethodthemethodusedtoperformthecalculation,either"raw"or"laplace"DetailsThisisaninternalfunction,andisnotmeanttobecalleddirectly.Howeverithasbeenexportedjustincase. 4comparisonValuealistwithtwoitems:LR.cal.sscalibratedLRsforthecomparisonforsamesetLR.cal.dscalibratedLRsforthecomparisonfordifferentsetAuthor(s)DavidLucyReferencesD.RamosandJ.Gonzalez-Rodrigues,(2008)"Cross-entropyanalysisoftheinformationinforensicspeakerrecognition,"inProc.IEEEOdyssey,SpeakerLang.Recognit.Workshop.SeeAlsoisotone::gpava(),calc.ece() comparisoncomparison:Apackageforcomputinglikelihoodratiosforunivariateandmultivariateevidence. DescriptionThispackageisforcomputingtheweightoftheevidence,i.e.thelikelihoodratio(LR)fortraceevidencewhichhasbeenquantiedwithsomeinstrument.Forexampleaforensicscientistmightbehavedeterminedtherefractiveindicesoffragmentsofglasstakenfromacrimesceneandfragmentsofglassrecoveredfromtheclothingofthesuspectedbreaker.Thispackageevaluatestheprobability(density)oftheevidence,E,(theRIvaluesfromthetwosamples)underthehypothesisHpthattheyoriginatedfromthesamesource,andalternativelyunderthehypothesisHdthattheyoriginatedfromanothersource.TheLRistheratioofthesetwoquantities,i.e.LR=p(EjHp) p(EjHd).ALRwhichisgreaterthanoneindicatesthattheevidencesupportsHp,andaLRwhichislessthanoneindicatesthattheevidencesupportsHd.DetailsThecomputationcanuseeitherunivariateormultivariateobservationsofaphysicalobject.Forex-ampletraceelementmeasurements,andasimilarsetofuni/multivariateobservationsfromanotherobject,andcalculatesalikelihoodratioforthepropositionsthattherstitemcamefromthesamesourceasthesecondgivensomepopulationdata. glass5Acknowledgements:Inapackageoffunctionssuchasthesewhichhaveundergonealongdevelopmentoveranum-berofyears,itisinevitablethatanumberofpeople,besidesthosedirectlycited,havehelpedtocorrectandaddtothecode.Thesepeopleare(inalphabeticalorder):IvoAlberink(NFI),AnabelBolck(NFI),SonjaMenges(BKA),GeoffMorrison(Aston),TerezaNeocleous(Glasgow),An-dersNordgaard(SKL),BradPatterson(GeorgeMason),PhilRose(ANU),AgnieszkaRzepecka(Jagiellonian),MarjanSjerps(NFI)andHanjingZhang(Edinburgh).ReferencesAitken,C.G.G.&Lucy,D.(2004)Evaluationoftraceevidenceintheformofmultivariatedata.AppliedStatistics:53(1):109-122. glassGlasscompositiondataforsevenelementsfrom200glassitems. DescriptionThesedataarefromGrzegorz(Greg)ZadoraattheInstituteofForensicResearchinKrakow,Poland.Theyarethelogoftheratiosofeachelementtooxygen,sologNaOisthelog(10)oftheSodiumtoOxygenratio,andlogAlOisthelogoftheAluminiumtoOxygenratio.Theinstru-mentalmethodwasSEM-EDX.Usagedata(glass)Formatadata.framewith2400rowsand9columns.itemfactor200levels-whichitemthemeasurementscamefromfragmentfactor4levels-whichofthefourfragmentsfromeachitemtheobservationsweremadeuponlogNaOnumericlogofsodiumconcentrationtooxygenconcentrationlogMgOnumericlogofmagnesiumconcentrationtooxygenconcentrationlogAlOnumericlogofaluminiumconcentrationtooxygenconcentrationlogSiOnumericlogofsiliconconcentrationtooxygenconcentrationlogKOnumericlogofpotassiumconcentrationtooxygenconcentrationlogCaOnumericlogofcalciumconcentrationtooxygenconcentrationlogFeOnumericlogofironconcentrationtooxygenconcentration 6plot.eceDetailsTheitemindicatestheobjecttheglasscamefrom.Thelevelsforeachitemareuniquetothatitem.Thefragmentcanbeconsideredasub-item.WhencollectingtheseobservationsGregtookaglassobject,sayajamjar,hewouldthenbreakit,andextractfourfragments.Eachfragmentwouldbemeasuredthreetimesupondifferentpartsofthatfragment.Thefragmentlabelsarerepeated,so,forexample,fragment"f1"fromitem"s2"hasnothingwhatsoevertodowithfragment"f1"fromitem"s101".Fortwolevelmodelsuseitemasthelowerlevel-threelevelmodelscanusetheadditionalinfor-mationfromtheindividualfragments.SourceGrzegorzZadoraInstituteofForensicResearch,Krakow,Poland.ReferencesAitken,C.G.G.Zadora,G.&Lucy,D.(2007)ATwo-LevelModelforEvidenceEvaluation.JournalofForensicSciences:52(2);412-419. plot.eceAnS3plotmethodforobjectsofclassece DescriptionAnS3plotmethodforobjectsofclasseceUsage##S3methodforclass'ece'plot(x,...)ArgumentsxanS3objectofclassecewhichisgeneratedfromcalc.ece()....otherargumentsthatarepassedtotheplotgeneric.Author(s)DavidLucySeeAlsocalc.ece() two.level.comparison.items7 two.level.comparison.itemsCreateacompitemobject. DescriptionThisfunctioncreatesacompitemobjectfromadata.frameormatrixofobservationsfromanitemtobedeemedacontrol,orarecovered,item.Usagetwo.level.comparison.items(data,data.columns)Argumentsdataamatrixordata.frameofobservedpropertiesfromeitherthecontrolitem,ortherecovereditemdata.columnsvectorofintegersgivingwhichcolumnsindataaretheobservationsofthepropertiesValueanobjectofclasscompitemExamples#loadGregZadora'sglassdatadata(glass)#calculateacompitemobjectrepresentingthecontrolitemcontrol=two.level.comparison.items(glass[1:6,],c(7,8,9)) two.level.componentsComputeintegratedmeansandcovariances DescriptionTakesalargesamplefromthebackgroundpopulationandcalculatesthewithinandbetweencovari-ancematrices,avectorofmeans,avectorofthecountsofreplicatesforeachitemfromthesample,andotherbitsneededtomakeupacompcovarobject.Usagetwo.level.components(data,data.columns,item.column) 8two.level.density.LRArgumentsdataamatrix,ordata.frame,ofobservations,withcasesinrows,andpropertiesascolumnsdata.columnsavectorindicatingwhichcolumnsarethepropertiesitem.columnanintegerindicatingwhichcolumngivestheitemDetailsUsesMLestimationatthemoment-thiswillalmostcertainlychangeinthefutureandhopefullyallowregularisationmethodstogetamorestable(andnon-singular)estimate.ValueanobjectofclasscompvarExamples#loadGregZadora'sglassdatadata(glass)#calculateacompcovarobjectbaseduponglas#usingK,CaandFe-warning-couldtaketime#onslowermachinesZ=two.level.components(glass,c(7,8,9),1) two.level.density.LRCalculatethelikelihoodratiousingmultivariateKDEs DescriptionTakesacompitemobjectwhichrepresentssomecontrolitem,andacompitemobjectwhichrep-resentsarecovereditem,thenusesinformationfromacompcovarobject,whichrepresentstheinformationfromthepopulation,tocalculatealikelihoodratioasameasureoftheevidencegivenbytheobservationsforthesame/differentsourcepropositions.Usagetwo.level.density.LR(control,recovered,background)ArgumentscontrolacompitemobjectwiththecontroliteminformationrecoveredacompitemobjectwiththerecoverediteminformationbackgroundacompcovarobjectwiththepopulationinformationValueanestimateofthelikelihoodratio two.level.lindley.LR9ReferencesAitken,C.G.G.&Lucy,D.(2004)Evaluationoftraceevidenceintheformofmultivariatedata.AppliedStatistics:53(1);109-122.Exampleslibrary(comparison)#loadGregZadora'sglassdatadata(glass)#calculateacompcovarobjectbaseduponglass#usingK,CaandFe-warning-couldtaketime#onslowermachinesZ=two.level.components(glass,c(7,8,9),1)#calculateacompitemobjectrepresentingthecontrolitemcontrol=two.level.comparison.items(glass[1:6,],c(7,8,9))#calculateacompitemobjectrepresentingtherecovereditem#knowntobefromthesameitem(item1)recovered.1=two.level.comparison.items(glass[7:12,],c(7,8,9))#calculateacompitemobjectrepresentingtherecovereditem#knowntobefromadifferentitem(item2)recovered.2=two.level.comparison.items(glass[19:24,],c(7,8,9))#calculatethelikelihoodratioforaknown#samesourcecomparison-shouldbe20.59322#2020-08-01Boththisversionandthepreviousversionreturn20.58967lr.1=two.level.density.LR(control,recovered.1,Z)lr.1#calculatethelikelihoodratioforaknown#differentsourcecomparison-shouldbe0.02901532#2020-08-01Boththisversionandthepreviousversionreturn0.01161392lr.2=two.level.density.LR(control,recovered.2,Z)lr.2 two.level.lindley.LRLikelihoodratiocalculationusingLindley'sapproach DescriptionTakesacompitemobjectwhichrepresentssomecontrolitem,andacompitemobjectwhichrep-resentsarecovereditem,thenusesinformationfromacompcovarobject,whichrepresentstheinformationfromthepopulation,tocalculatealikelihoodratioasameasureoftheevidencegivenbytheobservationsforthesame/differentsourcepropositions. 10two.level.lindley.LRUsagetwo.level.lindley.LR(control,recovered,background)ArgumentscontrolacompitemobjectwiththecontroliteminformationrecoveredacompitemobjectwiththerecoverediteminformationbackgroundacompcovarobjectwiththepopulationinformationDetailsDoesthelikelihoodratiocalculationsforatwo-levelmodelassumingthatthebetweenitemdistri-butionisunivariatenormal.ThisfunctionistakenfromtheapproachdevisedbyDenisLindleyinhis1977paper(detailsbelow)andrepresentstheprogenitorofallthefunctionsinthispackage.ValueanestimateofthelikelihoodratioAuthor(s)DavidLucyReferencesLindley,D.(1977)AprobleminforensicScience.Biometrika:64;207-213.Examples#loadGregZadora'sglassdatadata(glass)#calculateacompcovarobjectbasedupondat#usingKZ=two.level.components(glass,7,1)#calculateacompitemobjectrepresentingthecontrolitemcontrol=two.level.comparison.items(glass[1:6,],7)#calculateacompitemobjectrepresentingtherecovereditem#knowntobefromthesameitem(item1)recovered.1=two.level.comparison.items(glass[7:12,],7)#calculateacompitemobjectrepresentingtherecovereditem#knowntobefromadifferentitem(item2)recovered.2=two.level.comparison.items(glass[19:24,],7)#calculatethelikelihoodratioforaknown#samesourcecomparison-shouldbe6.323941 two.level.normal.LR11#Thisvalueis6.323327inthisversionandinthelastversionwrittenbyDavid(1.0-4)lr.1=two.level.lindley.LR(control,recovered.1,Z)lr.1#calculatethelikelihoodratioforaknown#differentsourcecomparison-shouldbe0.004422907#Thisvalueis0.004421978inthisversionandthelastversionwrittenbyDavid(1.0-4)lr.2=two.level.lindley.LR(control,recovered.2,Z)lr.2 two.level.normal.LRLikelihoodratiocalculation-normal DescriptionTakesacompitemobjectwhichrepresentssomecontrolitem,andacompitemobjectwhichrep-resentsarecovereditem,thenusesinformationfromacompcovarobject,whichrepresentstheinformationfromthepopulation,tocalculatealikelihoodratioasameasureoftheevidencegivenbytheobservationsforthesame/differentsourcepropositions.Usagetwo.level.normal.LR(control,recovered,background)ArgumentscontrolacompitemobjectwiththecontroliteminformationrecoveredacompitemobjectwiththerecoverediteminformationbackgroundacompcovarobjectwiththepopulationinformationDetailsDoesthelikelihoodratiocalculationsforatwo-levelmodelassumingthatthebetweenitemdistri-butionisuni/multivariatenormal.ValueanestimateofthelikelihoodratioAuthor(s)AgnieszkaMartynaandDavidLucyReferencesAitken,C.G.G.&Lucy,D.(2004)Evaluationoftraceevidenceintheformofmultivariatedata.AppliedStatistics:53(1);109-122. 12two.level.normal.LRExamples#loadGregZadora'sglassdatadata(glass)#calculateacompcovarobjectbaseduponglass#usingK,CaandFe-warning-couldtaketime#onslowermachinesZtwo.level.components(glass,c(7,8,9),1)#calculateacompitemobjectrepresentingthecontrolitemcontroltwo.level.comparison.items(glass[1:6,],c(7,8,9))#calculateacompitemobjectrepresentingtherecovereditem#knowntobefromthesameitem(item1)recovered.1two.level.comparison.items(glass[7:12,],c(7,8,9))#calculateacompitemobjectrepresentingtherecovereditem#knowntobefromadifferentitem(item2)recovered.2two.level.comparison.items(glass[19:24,],c(7,8,9))#calculatethelikelihoodratioforaknown#samesourcecomparison-shouldbe51.16539#Thisvalueis51.14243inthisversionandthelastversionDavidwrote(1.0-4)lr.1two.level.normal.LR(control,recovered.1,Z)lr.1#calculatethelikelihoodratioforaknown#differentsourcecomparison-shouldbe0.02901532#Thisvsalueis0.02899908inthisversionandthelastversionDavidwrote(1.0-4)lr.2two.level.normal.LR(control,recovered.2,Z)lr.2 Indexdatasetsglass,5multivariatecomparison,4packagecomparison,4calc.ece,2calc.ece(),4,6calibrate.set,3calibrate.set(),3comparison,4glass,5isotone::gpava(),3,4plot.ece,6two.level.comparison.items,7two.level.components,7two.level.density.LR,8two.level.lindley.LR,9two.level.normal.LR,1113