LectureNotesinArtificialIntelligence9978
SubseriesofLectureNotesinComputerScience
LNAISeriesEditors
RandyGoebel UniversityofAlberta,Edmonton,Canada
YuzuruTanaka HokkaidoUniversity,Sapporo,Japan
WolfgangWahlster
DFKIandSaarlandUniversity,Saarbrücken,Germany
LNAIFoundingSeriesEditor
JoergSiekmann
DFKIandSaarlandUniversity,Saarbrücken,Germany
Moreinformationaboutthisseriesathttp://www.springer.com/series/1244
Van-NamHuynh • MasahiroInuiguchi
BacLe • BaoNguyenLe
ThierryDenoeux(Eds.)
5thInternationalSymposium,IUKM2016 DaNang,Vietnam,November30 – December2,2016
Proceedings
IntegratedUncertainty inKnowledgeModelling andDecisionMaking
123
Editors
Van-NamHuynh
JapanAdvancedInstituteofScience andTechnology
Nomi,Ishikawa Japan
MasahiroInuiguchi
GraduateSchoolofEngineeringScience
OsakaUniversity Toyonaka,Osaka Japan
BacLe UniversityofScience
HoChiMinhCity Vietnam
BaoNguyenLe DuyTanUniversity DaNang Vietnam
ThierryDenoeux
Université deTechnologiedeCompiègne
Compiègne France
ISSN0302-9743ISSN1611-3349(electronic)
LectureNotesinArtificialIntelligence
ISBN978-3-319-49045-8ISBN978-3-319-49046-5(eBook) DOI10.1007/978-3-319-49046-5
LibraryofCongressControlNumber:2016955999
LNCSSublibrary:SL7 – ArtificialIntelligence
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Preface
Thisvolumecontainsthepapersthatwerepresentedatthe5thInternationalSymposiumonIntegratedUncertaintyinKnowledgeModellingandDecisionMaking(IUKM 2016)heldinDaNang,Vietnam,fromNovember30toDecember2,2016.
TheIUKMsymposiaaimtoprovideaforumfortheexchangeofresearchresults andideas,andexperiencesinapplicationamongresearchersandpractitionersinvolved withallaspectsofuncertaintymodellingandmanagement.Previouseditionsofthe conferencewereheldinIshikawa,Japan(originallyunderthenameofInternational SymposiumonIntegratedUncertaintyManagementandApplications – IUM2010), Hangzhou,China(IUKM2011),Beijing,China(IUKM2013),andNhaTrang, Vietnam(IUKM2015).
IUKM2016wasjointlyorganizedbyDuyTanUniversity(DaNang,Vietnam), JapanAdvancedInstituteofScienceandTechnology(JAIST),andBeliefFunctions andApplicationsSociety(BFAS).
Theorganizersreceived78submissions.Eachofwhichwaspeerreviewedbyat leasttwomembersoftheProgramCommittee.While35paperswereacceptedafterthe firstroundofreviews,22otherswereconditionallyacceptedandunderwentarebuttal stageinwhichauthorswereaskedtorevisetheirpaperinaccordancetothereviews, andprepareanextensiveresponseaddressingthereviewers’ concerns.The final decisionwasmadebytheprogramchairs.Finally,57paperswereacceptedforpresentationatIUKM2016andpublicationintheproceedings.Invitedtalkspresentedat thesymposiumarealsoincludedinthisvolume.
Asafollow-upofthesymposium,aspecialvolumeofthe InternationalJournalof ApproximateReasoning isanticipatedtoincludeasmallnumberofextendedpapers selectedfromthesymposiumaswellasotherrelevantcontributionsreceivedin responsetosubsequentopencalls.Thesejournalsubmissionswillgothroughafresh roundofreviewsinaccordancewiththejournal’sguidelines.
TheIUKM2016symposiumwaspartiallysupportedbytheNationalFoundationfor ScienceandTechnologyDevelopmentofVietnam(NAFOSTED)andDuyTan University.TheIUKM2016beststudentpaperawardwassponsoredbyElsevier.We areverythankfultoDr.Gia-NhuNguyenandhislocalorganizingteamfromDuyTan Universityfortheirhardworkandefficientservicesandforthewonderfullocal arrangements.
WewouldliketoexpressourappreciationtothemembersoftheProgramCommitteefortheirsupportandcooperationinthispublication.Wearealsothankfulto AlfredHofmann,AnnaKramer,andtheircolleaguesatSpringerforprovidinga meticulousserviceforthetimelyproductionofthisvolume.Last,butcertainlynotthe
least,ourspecialthanksgotoalltheauthorswhosubmittedpapersandalltheattendees fortheircontributionsandfruitfuldiscussionsthatmadethisconferenceagreat success.
December2016Van-NamHuynh MasahiroInuiguchi BacLe BaoN.Le ThierryDenoeux
VIPreface
Organization
GeneralCo-chairs
BaoN.LeDuyTanUniversity,DaNang,Vietnam ThierryDenoeuxUniversityofTechnologyofCompiègne,France
HonoraryCo-chairs
MichioSugenoEuropeanCenterforSoftComputing,Spain HungT.NguyenNewMexicoStateUniversity,USA; ChiangMaiUniversity,Thailand CoC.LeDuyTanUniversity,DaNang,Vietnam SadaakiMiyamotoUniversityofTsukuba,Japan
ProgramCo-chairs
Van-NamHuynhJAIST,Japan
MasahiroInuiguchiUniversityofOsaka,Japan
BacLeUniversityofScience,VNU-HoChiMinh,Vietnam
LocalArrangementsChair
Gia-NhuNguyenDuyTanUniversity,DaNang,Vietnam
PublicationandFinancialChair
Van-HaiPhamPaci ficOceanUniversity,NhaTrang,Vietnam
ProgramCommittee
Byeong-SeokAhnChung-AngUniversity,Korea YaxinBiUniversityofUlster,UK
Bernadette Bouchon-Meunier Université PierreetMarieCurie,France
LamThuBuiLeQuyDonTechnicalUniversity,Vietnam HumbertoBustinceUniversidadPublicadeNavarra,Spain TruCaoHoChiMinhCityUniversityofTechnology,Vietnam FabioCuzzolinOxfordBrookesUniversity,UK
Tien-TuanDaoUniversityofTechnologyofCompiègne,France
BernardDeBaetsGhentUniversity,Belgium YongDengXianJiaotongUniversity,China
ThierryDenoeuxUniversityofTechnologyofCompiègne,France
SebastienDesterckeUniversityofTechnologyofCompiègne,France
KarimElKiratUniversityofTechnologyofCompiègne,France
ZiedElouediLARODEC,ISGdeTunis,Tunisie TomoeEntaniUniversityofHyogo,Japan
LluisGodoIIIA-CSIC,Spain
FernandoGomideUniversityofCampinas,Brazil
PeijunGuoYokohamaNationalUniversity,Japan EnriqueHerrera-ViedmaUniversityofGranada,Spain
Marie-ChristineHo BaTho UniversityofTechnologyofCompiègne,France
KatsuhiroHondaOsakaPrefectureUniversity,Japan Tzung-PeiHongNationalUniversityofKaohsiung,Taiwan
VanNamHuynhJAIST,Japan
MasahiroInuiguchiOsakaUniversity,Japan
RadimJirousekUniversityofEconomics,CzechRepublic JanuszKacprzykPolishAcademyofSciences,Poland
GabrieleKern-IsbernerTechnischeUniversitätDortmund,Germany
EtienneKerreGhentUniversity,Belgium
LaszloT.KoczyBudapestUniversityofTechnologyandEconomics, Hungary
VladikKreinovichUniversityofTexasatElPaso,USA RudolfKruseUniversityofMagdeburg,Germany
YasuoKudoMuroranInstituteofTechnology,Japan YoshifumiKusunokiOsakaUniversity,Japan
JonathanLawryUniversityofBristol,UK
Anh-CuongLeTonDucThangUniversity,Vietnam BacLeUniversityofScience,VNU-HoChiMinh,Vietnam Churn-JungLiauAcademiaSinica,Taipei,Taiwan
Chin-TengLinNationalChiao-TungUniversity,Taiwan JunLiuUniversityofUlster,UK
WeiruLiuQueen’sUniversityBelfast,UK
AnitawatiMohd Lokman UniversitiTeknologiMARA(UiTM)Malaysia
TiejuMaEastChinaUniversityofScienceandTechnology,China
CatherineK.MarqueUniversityofTechnologyofCompiègne,France LuisMartinezUniversityofJaen,Spain
RadkoMesiarSlovakUniversityofTechnologyinBratislava,Slovakia
TetsuyaMuraiHokkaidoUniversity,Japan
CanhHaoNguyenKyotoUniversity,Japan ThanhBinhNguyenDuyTanUniversity,Vietnam;IIASA,Austria LeMinhNguyenJAIST,Japan
HungSonNguyenUniversityofWarsaw,Poland XuanHoaiNguyenHanoiUniversity,Vietnam
ThanhHienNguyenTonDucThangUniversity,Vietnam AkiraNotsuOsakaPrefectureUniversity,Japan
VIIIOrganization
VilemNovakOstravaUniversity,CzechRepublic NikhilPalIndianStatisticalInstitute,India
IrinaPerfilievaOstravaUniversity,CzechRepublic TuanPhung-DucTokyoInstituteofTechnology,Japan ZengchangQinBeihangUniversity,China YasuoSasakiJAIST,Japan
HirosatoSekiOsakaUniversity,Japan
DominikSlezakUniversityofWarsawandInfobrightInc.,Poland NoboruTakagiToyamaPrefecturalUniversity,Japan YongchuanTangZhejiangUniversity,China
Phantipa
Thipwiwatpotjana
ChulalongkornUniversity,Thailand
VicencTorraUniversityofSkovde,Sweden
SeikiUbukataOsakaUniversity,Japan
BayVoHUTECH,Vietnam
GuoyinWangChongqingUniversityofPostsandTelecom.,China
Thanuka
Wickramarathne UniversityofMassachusetts,USA
ZeshuiXuSichuanUniversity,China
Hong-BinYanEastChinaUniversityofScienceandTechnology,China ChunlaiZhouRenminUniversityofChina
LocalOrganizingCommittee
VietHungDangDuyTanUniversity,DaNang,Vietnam VanSonPhanDuyTanUniversity,DaNang,Vietnam PhungHoiPhanDuyTanUniversity,DaNang,Vietnam ThanhDuongNguyenDuyTanUniversity,DaNang,Vietnam DucManNguyenDuyTanUniversity,DaNang,Vietnam ThoaiMyHoDuyTanUniversity,DaNang,Vietnam NgocTrungDangDuyTanUniversity,DaNang,Vietnam VuTienTruongDuyTanUniversity,DaNang,Vietnam DacNhuongLeHaiPhongUniversity,HaiPhong,Vietnam
OrganizationIX
FuzzyCo-clusteringandApplication toCollaborativeFiltering
KatsuhiroHonda
OsakaPrefectureUniversity,Sakai,Japan
Shortbiography: KatsuhiroHondaisaprofessoroftheDepartmentofComputer ScienceandIntelligentSystems,GraduateSchoolofEngineering,OsakaPrefecture University,Japan.Hisresearchinterestsincludehybridtechniquesoffuzzyclustering andmultivariateanalysis,dataminingwithfuzzydataanalysis,andneuralnetworks. Hehaspublishedmorethan100scientificpapers,includingthoseappearinginsuch journalsasIEEETransactionsonFuzzySystems,InternationalJournalofApproximate Reasoning,etc.HereceivedtheOutstandingBookAward(2010),theBestPaper Award(2002,2011,2012)andsoonfromtheJapanSocietyforFuzzyTheoryand IntelligentInformatics,anddeliveredatutoriallectureatthe2004IEEEInternational ConferenceonFuzzySystems.
Summary: Cooccurrenceinformationanalysisbecamemorepopularinmanywebbasedsystemanalysissuchasdocumentanalysisorpurchasehistoryanalysis.Rather thantheconventionalmultivariateobservations,eachobjectischaracterizedbyits cooccurrencedegreeswithvariousitems,andthegoalisoftentoextractco-cluster structuresamongobjectsanditems,suchthatmutuallyfamiliarobject-itempairsform aco-cluster.Atypicalapplicationofco-clusterstructureanalysiscanbeseenincollaborative filtering(CF).CFisabasictechniqueforachievingpersonalizedrecommendationinvariouswebservicesbyconsideringthesimilarityofpreferencesamong users.Inthistalk,I’dliketointroduceafuzzyco-clusteringmodel,whichismotivated fromastatisticalco-clusteringmodel,anddemonstrateitsapplicabilitytoCFtasks followingabriefreviewoftheCFframework.
Contents
InvitedPapers
OnEvidentialMeasuresofSupportforReasoningwithIntegrated Uncertainty:ALessonfromtheBanofP-valuesinStatisticalInference.....3 HungT.Nguyen
FuzzyCo-ClusteringandApplicationtoCollaborativeFiltering..........16 KatsuhiroHonda
EvidentialClustering:AReview................................24 ThierryDenœuxandOrakanyaKanjanatarakul
UncertaintyManagementandDecisionSupport
Non-uniquenessofIntervalWeightVectortoConsistentIntervalPairwise ComparisonMatrixandLogarithmicEstimationMethods...............39 MasahiroInuiguchi
SequentialDecisionProcessSupportedbyaCompositionalModel........51 RadimJiroušekandLucieVáchová
ATheoryofModelingSemanticUncertaintyinLabelRepresentation......64 ZengchangQin,TaoWan,andHanqingZhao
AProbabilityBasedApproachtoEvaluationofNewEnergyAlternatives...76 Hong-BinYan
MinimaxRegretRelaxationProcedureofExpectedRecourseProblem withVectorsofUncertainty...................................89 ThibhadhaSaraprangandPhantipaThipwiwatpotjana
BottomUpReviewofCriteriainHierarchicallyStructuredDecision Problem.................................................99 TomoeEntani
ATwo-StageFuzzyQualityFunctionDeploymentModelforService Design..................................................110 Hong-BinYan,ShaojingCai,andMingLi
UsagesofFuzzyReturnsonMarkowitz’sPortfolioSelection............124 TanaratRattanadamrongaksorn,JirakomSirisrisakulchai, andSongsakSriboonjitta
AFloodRiskAssessmentBasedonMaximumFlowCapacityofCanal System.................................................136
JirakomSirisrisakulchai,NapatHarnpornchai, KittawitAutchariyapanitkul,andSongsakSriboonchitta
SoftClusteringandClassification
GeneralizationsofFuzzy c-MeansandFuzzyClassifiers...............151
SadaakiMiyamoto,YoshiyukiKomazaki,andYasunoriEndo
PartialDataQueryingThroughRacingAlgorithms...................163
Vu-LinhNguyen,SébastienDestercke,andMarie-HélèneMasson
FuzzyDAClustering-BasedImprovementofProbabilisticLatentSemantic Analysis.................................................175
TakafumiGoshima,KatsuhiroHonda,SeikiUbukata,andAkiraNotsu
ExclusiveItemPartitionwithFuzzinessTuninginMMMs-InducedFuzzy Co-clustering.............................................185
TakayaNakano,KatsuhiroHonda,SeikiUbukata,andAkiraNotsu
AHybridModelofARIMA,ANNsand k-MeansClusteringforTime SeriesForecasting..........................................195
WarutPannakkong,VanHaiPham,andVan-NamHuynh
TheRoughMembership k-MeansClustering.......................207
SeikiUbukata,AkiraNotsu,andKatsuhiroHonda
InstanceReductionforTimeSeriesClassificationbyExploiting RepresentativeCharacteristicsusingk-means.......................217 VoThanhVinh,HienT.Nguyen,andTinT.Tran
ANewFaultClassificationSchemeUsingVibrationSignalSignatures andtheMahalanobisDistance..................................230 JaeyoungKim,HungNguyenNgoc,andJongmyonKim
MachineLearningforSocialMediaAnalytics
EstimatingAsymmetricProductAttributeWeightsinReviewMining......245 WeiOu,Anh-CuongLe,andVan-NamHuynh
DeepBi-directionalLongShort-TermMemoryNeuralNetworks forSentimentAnalysisofSocialData............................255
NgocKhuongNguyen,Anh-CuongLe,andHongThaiPham
LinguisticFeaturesandLearningtoRankMethodsforShoppingAdvice....269 Xuan-HuyNguyenandLe-MinhNguyen
XXContents
AnEvidentialMethodforMulti-relationalLinkPredictioninUncertain SocialNetworks...........................................280
SabrineMallek,ImenBoukhris,ZiedElouedi,andEricLefevre
DetectingThaiMessagesLeadingtoDeceptiononFacebook............293 PanidaSongram,AtcharaChoompol,PaitoonThipsanthia, andVeeraBoonjing
AnswerValidationforQuestionAnsweringSystemsbyUsingExternal Resources................................................305 Van-TuNguyenandAnh-CuongLe
OptimizingSelectionofPZMIFeaturesBasedonMMASAlgorithm forFaceRecognitionoftheOnlineVideoContextualAdvertisement User-OrientedSystem.......................................317 BaoNguyenLe,Dac-NhuongLe,GiaNhuNguyen,andDoNangToan Phrase-BasedCompressiveSummarizationforEnglish-Vietnamese........331 TungLe,Le-MinhNguyen,AkiraShimazu,andDinhDien
ImprovethePerformanceofMobileApplicationsBasedonCode OptimizationTechniquesUsingPMDandAndroidLint................343 ManD.Nguyen,ThangQ.Huynh,andT.HungNguyen
BiomedicalandImageApplications
ClusteringofChildrenwithCerebralPalsywithPriorBiomechanical KnowledgeFusedfromMultipleDataSources......................359 TuanNhaHoang,TienTuanDao,andMarie-ChristineHoBaTho Co-SimulationofElectricalandMechanicalModelsoftheUterineMuscle...371 MaximeYochum,JérémyLaforêt,andCatherineMarque
ComputingEHGSignalsfromaRealistic3DUterusModel: AMethodtoAdaptaPlanarVolumeConductor.....................381 MaximeYochum,PamelaRiahi,JérémyLaforêt,andCatherineMarque
AntColonyOptimizationBasedAnisotropicDiffusionApproachfor DespecklingofSARImages...................................389 VikrantBhateja,AbhishekTripathi,AditiSharma,BaoNguyenLe, SureshChandraSatapathy,GiaNhuNguyen,andDac-NhuongLe AFusionofBagofWordModelandHierarchicalK-Means++ inImageRetrieval..........................................397 MyKieu,KhaiDinhLai,TamDucTran,andThaiHoangLe
ContentsXXI
AcceleratingEnvelopeAnalysis-BasedFaultDiagnosis UsingaGeneral-PurposeGraphicsProcessingUnit...................409 VietTra,SharifUddin,JaeyoungKim,Cheol-HongKim, andJongmyonKim
TheMarkerDetectionfromProductLogoforAugmentedReality Technology..............................................421 ThummaratBoonrod,PhatthanaphongChomphuwiset, andChatklawJareanpon
DataMiningandApplication
AnApproachtoDecreaseExecutionTimeandDifferenceforHidingHigh UtilitySequentialPatterns....................................435 MinhNguyenQuang,UtHuynh,TaiDinh,NghiaHoaiLe,andBacLe
ModelingGlobal-scaleDataMartsBasedonFederatedDataWarehousing ApplicationFramework......................................447 NgocSyNgoandBinhThanhNguyen
HowtoSelectanAppropriateSimilarityMeasure:TowardsaSymmetryBasedApproach...........................................457 IldarBatyrshin,ThongchaiDumrongpokaphan,VladikKreinovich, andOlgaKosheleva
AConvexCombinationMethodforLinearRegressionwithIntervalData...469 SomsakChanaim,SongsakSriboonchitta,andChongkolneeRungruang
ACopula-BasedMarkovSwitchingSeeminglyUnrelatedRegression ApproachforAnalysistheDemandandSupplyonSugarMarket.........481 PathairatPastpipatkul,NisitPanthamit,WoraphonYamaka, andSongsakSriboochitta
TheBestCopulaModelingofDependenceStructureAmongGold,Oil Prices,andU.S.Currency....................................493 PathairatPastpipatkul,ParaveeManeejuk,andSongsakSriboonchitt
ModelingandForecastingInterdependenceoftheASEAN-5StockMarkets andtheUS,JapanandChina..................................508 KritLattayaporn,JianxuLiu,JirakomSirisrisakulchai, andSongsakSriboonchitta
XXIIContents
StatisticalMethods
NeedforMostAccurateDiscreteApproximationsExplainsEffectiveness ofStatisticalMethodsBasedonHeavy-TailedDistributions.............523 SongsakSriboonchitta,VladikKreinovich,OlgaKosheleva, andHungT.Nguyen
ANewMethodforHypothesisTestingUsingInferentialModels withanApplicationtotheChangepointProblem.....................532 SonPhucNguyen,UyenHoangPham,ThienDinhNguyen, andHoaThanhLe
ConfidenceIntervalsfortheRatioofCoefficientsofVariation intheTwo-ParameterExponentialDistributions.....................542 PatarawanSangnawakij,Sa-AatNiwitpong,andSuparatNiwitpong
SimultaneousFiducialGeneralizedConfidenceIntervalsforAllDifferences ofCoefficientsofVariationofLog-NormalDistributions...............552 WarisaThangjai,Sa-AatNiwitpong,andSuparatNiwitpong
ConfidenceIntervalsforCommonVarianceofNormalDistributions.......562 NarudeeSmithpreecha,Sa-AatNiwitpong,andSuparatNiwitpong
ConfidenceIntervalsforCommonMeanofNormalDistributions withKnownCoefficientofVariation.............................574 SukrittaSodanin,Sa-AatNiwitpong,andSuparatNiwitpong
PairTradingRulewithSwitchingRegressionGARCHModel...........586 KongliangZhu,WoraphonYamaka,andSongsakSriboonchitta
EconometricApplications
AnEmpiricalConfirmationoftheSuperiorPerformanceofMIDAS overARIMAX............................................601 TanapornTungtrakul,NatthaphatKingnetr,andSongsakSriboonchitta
ModellingCo-movementandPortfolioOptimizationofGold andGlobalMajorCurrencies..................................612 MethasRattanasorn,JianxuLiu,JirakomSirisrisakulchai, andSongsakSriboonchitta
DoesAsianCreditDefaultSwapIndexImprovePortfolioPerformance?....624 ChatchaiKhiewngamdee,WoraphonYamaka, andSongsakSriboonchitta
ACopula-BasedStochasticFrontierModelandEfficiencyAnalysis: EvidencefromStockExchangeofThailand........................637 PhachongchitTibprasorn,SomsakChanaim,andSongsakSriboonchitta
ContentsXXIII
EconomicGrowthandIncomeInequality:EvidencefromThailand........649 ParaveeManeejuk,PathairatPastpipatkul,andSongsakSriboonchitta
Thailand’sExportandASEANEconomicIntegration:AGravityModel withStateSpaceApproach....................................664 PathairatPastpipatkul,PetchaluckBoonyakunakorn, andSongsakSriboonchitta
VolatilityHedgingModelforPreciousMetalFuturesReturns............675 RoengchaiTansuchat,ParaveeManeejuk,andSongsakSriboonchitta
WhatFirmsMustPayBribesandHowMuch?AnEmpiricalStudyofSmall andMediumEnterprisesinVietnam.............................689 ThiThuongVuandChonVanLe
AnalysisofAgriculturalProductioninAsiaandMeasurementofTechnical EfficiencyUsingCopula-BasedStochasticFrontierQuantileModel........701 VarithPipitpojanakarn,ParaveeManeejuk,WoraphonYamaka, andSongsakSriboonchitta
StatisticalandANNApproachesinCreditRatingforVietnamese Corporate:AComparativeEmpiricalStudy........................715 HungNguyenandTungNguyen
AuthorIndex
............................................727 XXIVContents
InvitedPapers
HungT.Nguyen1,2(B)
1 DepartmentofMathematicalSciences,NewMexicoStateUniversity, LasCruces,USA hunguyen@nmsu.edu
2 FacultyofEconomics,ChiangMaiUniversity,ChiangMai,Thailand
Abstract. InviewoftherecentbanoftheuseofP-valuesinstatisticalinference,sincetheyarenotqualifiedasinformationmeasuresof supportfromempiricalevidence,wewillnotonlytakeacloserlookat them,butalsoembarkonapanoramaofmorepromisingingredients whichcouldreplaceP-valuesforstatisticalscienceaswellasforany fieldsinvolvingreasoningwithintegrateduncertainty.Theseingredients includetherecentlydevelopedtheoryofInferentialModels,theemergent InformationTheoreticStatistics,andofcourseBayesianstatistics.The lessonlearnedfromthebanofP-valuesisemphasizedforothertypesof uncertaintymeasures,whereinformationmeasures,theirlogicalaspects (conditionalevents,probabilitylogic)areexamined.
Keywords: Bayesianstatistics · Conditionalevents · Entropyinference procedures · Informationmeasures · Informationtheoreticstatistics · IntegrateduncertaintyprobabilitylogicP-values · Testinghypotheses
1Introduction
TherecentbanontheuseofthenotionofP-valuesinhypothesistesting(TrafimowandMarks[32])triggeredaseriousreexaminationofthewayweused toconductinferenceinthefaceofuncertainty.Sincestatisticaluncertaintyis animportantpartofanintegrateduncertaintysystem,acloserlookatwhat wentwrongwithstatisticalinferenceisnecessaryto“repair”thewholeinferencemachineryincomplexsystems.
Thus,thispaperisorganizedasfollows.Westartout,inSect. 2,by elaboratingonthenotionofP-valuesasatestingprocedureinnullhypothesissignficancetesting(NHST).InSect. 3,withinthecontextofreasoningwith uncertaintywherelogicalaspectsandinformationmeasuresareemphasized,we elaborateonwhyp-valuesshouldnotbeusedasaninferenceprocedureanymore.Section 4 addressesthequestion“Whataretheitemsinstatisticaltheory
c SpringerInternationalPublishingAG2016 V.-N.Huynhetal.(Eds.):IUKM2016,LNAI9978,pp.3–15,2016. DOI:10.1007/978-3-319-49046-5 1
OnEvidentialMeasuresofSupport forReasoningwithIntegratedUncertainty: ALessonfromtheBanofP-values inStatisticalInference
whichareaffectedbytheremovalofP-values?”.Section 5 pointsoutalternative inferenceproceduresinaworldwithoutP-values.WereservethelastSect. 6 for apossible“indefenseofP-values”.
2TheNotionofP-valuesinStatisticalInference
ItseemsusefultotracebackabitofFisher’sgreatachievementsinstatistical science.Thestorygoeslikethis.Aladyclaimedthatshecantellwhetheracupof teawithmilkwasmixedwithteaormilkfirst,R.Fisherdesignedanexperiment inwhicheightcupsofmixedtea/milk(fourofeachkind)waspresentedtoher (lettingherknowthatfourcupsaremixedwithmilkfirst,andtheotherfour aremixedwithteafirst)inarandomsequence,andaskedhertotasteandtell theorderofmixtureofallcups.Shegotalleightcorrectidentifications.How didFisherarriveattheconclusionthattheladyisindeedskillful?SeeFisher [10],alsoSalbursg[29].ThiskindoftestingproblemistermedNullHypothesis SignificanceTesting(NHST),duetoFisher[9].
Theimportantquestionis“CouldweuseP-valuestocarryoutNHST?”.You mayask“whatistherationaleforusingP-valuetomakeinference?”.Well,don’t youknowtheanswer?Itcouldbethe Cournot’sprinciple (see,e.g.,Shaferand Vork,[31],pp.44+),accordingtowhich,itispracticallycertainthatpredicted eventsofsmallprobabilitieswillnotoccur.Butitisjusta“principle”,nota theorem!Itdoeshavesomeflavoroflogic(forreasoning),butwhichlogic?See alsoGurevichandVovk[14],wheretwo“interesting”thingstobenoted:First, tocarryoutatest,onejust“adopts”a“convention”,namely“foragiventest, smallervaluesprovidestrongerimpugningevidence”!Andsecondly,itisafact that“everyteststatisticisequivalenttoauniqueexactP-valuefunction”.
3WhyP-valuesAreBanned?
StartingwithNHST,theuniquewaytoinferconclusionsfromdataisthetraditionalnotionofP-values.However,thereissomethingfishyabouttheuseof P-valuesasa“valid”inferenceprocedure,sincequitesometimesseriousproblemswiththemarised,exemplifiedbyCohen[6],Schervish[30],Goodman[13], HurlbertandLombardi[15],Lavine[16],andNuzzo[28].
HavingrelieduponP-valueastheinferenceproceduretocarryoutNHST (theirbreadandbutterresearchtool)forsolong,thePsychologycommunity finallyhasenoughofits“wrongdoings”,andwithoutanyreactionsfromthe internationalstatisticalcommunity(whichisresponsableforinventinganddevelopingstatisticaltoolsforallothersciencestouse),decided,ontheirown,toban NHST-Procedure(meaningP-values),TrafimowandMarks[32].Whilethisisa banonlyfortheirBasicandAppliedSocialPsychologyJournal,theimpactis worldwide.Itisnotaboutthe“ban”,itisabout“whatwrongwithP-values?” thatweshouldallbeconcerned.Foraflavorofdoingwrongstatistics,seee.g., Wheelan[34].
4H.T.Nguyen
Even,thebangetseverybody’sattentionnow,whathappendsincelastyear? Nothing!Why?EvenaftertheAmericanStatisticalAssociationissueda“statement”aboutP-values(ASANews[2]),andWasserteinandLazar[33],notbanningP-values(whynot?),but“stating”six“principles”.
Whatdoyoureadandexpectfromtheabove“statement”?Someliterature searchrevealsstufflikethis.“Togetherweagreedthatthe currentculture of statisticalsignificancetesting,interpretation,andreporting hastogo,andthat adherencetoaminimumofsixprinciplescanhelptopavethewayforwardfor scienceandsociety”.Andinthe SciencesNews,forlaymen,“P-valueban:small stepforajournal,giantleapforsicence”.Seealso,Lavine[16].
TherearethreetheoreticalfactswhichmakeP-valuesundesirableforstatisticalinference:
(i)P-valuesarenotmodelprobabilities.
First,observethatahypothesisisastatisticalmodel.TheP-value P (Tn ≥ t|Ho )istheprobabilityofobservingofanextremevalue t ifthenullhypothesis istrue.Itisnot P (Ho |Tn ≥ t)evenwhenthis“modelprobabilitygiventhe data”makessense(e.g.,asintheBayesianframeworkwhere Ho isviewedasa randomevent).Notethatwhen P (Ho |Tn ≥ t)makessenseandisavailable,it islegitimatetouseitformodelselection(avalidinferenceprocedurefromat leastacommonsensestandpoint).Inafrequentistframework,thereisnoway toconvert P (Tn ≥ t|Ho )to P (Ho |Tn ≥ t).Assuch,theP-value P (Tn ≥ t|Ho ), alone,isuselessforinference,preciselyas“stated”inthesixthprincipleof theASA.
(ii)ThereasoningwithP-valuesisbasedonaninvalidlogic.
AsmentionedbyCohen[6]andintheprevioussection,theuseofP-valuesto reject Ho seemstobebasedonaformofModusTollensinlogic,sinceafterall, reasoningunderuncertaintyisinference!and,eachmodeofreasoningisbased uponalogic.Now,thankstoArtificialIntelligence(AI),weareexposedtoa varietyoflogics,suchasprobabilitylogic,conditionalprobabilitylogic,fuzzy logics...whicharelogicsforreasoningundervarioustypesofuncertainty.Seea textlikeGoodman,NguyenandWalker[12].Inparticular,wecouldfacerules thathaveexceptions(seee.g.,Bamber,GoodmanandNguyen,[3]).Thefamous “penguintriangle”inAIcanbeusedtoillustratewelltheinvalidityofModus Tollensinuncertainlogics.
WhilewefocusinthisaddressonreasoningwithP-valuesinprobabilisticsystems,perhapsfewwordsaboutreasoningwithmorecomplexsystems inwhichseveraldifferenttypesofuncertaintyareinvolved(integrateduncertainsystems)shouldbementioned.Tocreatemachinescapableofevermore sophisticatedtasks,andofexhibitingevermorehuman-likebehavior,weneed knowledgerepresentationandassociatedreasoning(logic).Inprobabilisticsystems,noadditionalmathematicaltoolsareneeded,sincewearesimplydealing withprobabilitydistributions,andthelogicusedisclassicaltwo-valuedlogic. Forgeneralintegrateduncertainsystems,newmathematicaltoolssuchasconditionalevents,possibilitytheory,fuzzylogicsareneeded.See,e,g.,Nguyenand Walker[25],NguyenandWalker[26],Nguyen[27].
OnEvidentialMeasuresofSupportforReasoning5
(iii)Asset-functions,P-valuesarenotinformationmeasuresofmodelsupport.
Schervish[30],whilediscussingthe“usual”useofP-valuestotesthypotheses(inbothNHSTandNeyman-Pearsontests),“discovered”that“acommon informaluseofP-valuesasmeasuresofsupportorevidenceforhypotheseshas seriouslogicalflaws”.Wewillelaborateonhis“discovery”inthecontextof informationtheory.
Essentially,thereasontouseP-values,inthefirstplace,althoughnotstated explicitlyassuch,to“infer”conclusionsfromdata,isthattheyseemstobe “informationmeasuresoflocation”derivedfromdata(evidence)insupportof hypotheses.Isthattrue?Specifically,Givenanullhypothesis Ho andastatistic Tn andtheobservedvalue Tn = t,theP-value p(Ho )= P (Tn ≥ t|Ho ),as afunctionof Ho ,forfixed Tn andtheobservedvalue Tn = t,is“viewed”asa measureofsupportthattheobservedvalue t lendsto Ho (oramountofevidence infavorof Ho )sincelargevaluesof p(Ho )= P (Tn ≥ t|Ho )makeitharderto reject Ho (whereas,smallvaluesreflectnon-supportfor Ho ,i.e.,rejection).But this“practice”isalwaysinformal,and“notheoryiseverputforwardforwhat propertiesameasureofsupportorevidenceshouldhave”.
Whatisaninformationmeasure?Informationdecreasesuncertainty.Qualitativeinformationishighifsurpriseishigh.Whenanevent A isrealized,itprovides aninformation.Clearly,inthecontextof“statisticalinformationtheory”,informationisadecreasingfunctionofprobability:thesmallertheprobabilityfor A tooccur,thehighertheinformationobtainedwhen A isrealized.If A standsfor “snowing”,thenwhen A occured,say,inBangkok,itprovidesa“huge”amount ofinformation I (A).Putitmathematically(asinInformationTheory,seee.g., CoverandThomas,[7], I (A)= log P (A).Forageneraltheoryofinformation withoutprobability,butkeepingtheintuitivebehaviorthatinformationshould beadecreasingfunctionofevents,see,e.g.,Nguyen[24].Thisintuitivebehavior isaboutaspecificaspectofthenotionofinformationthatweareconsideringin uncertaintyanalysis,namely, informationoflocalization.
Inthecontextoftestingaboutaparametricmodel,say, f (x|θ ),θ ∈ Θ ,each hypothesis Ho canbeidentifiedwithasubsetof Θ ,stilldenotedas Ho ⊆ Θ Aninformationmeasureoflocationon Θ isaset-function I :2Θ → R+ such that A ⊆ B =⇒ I (A) ≥ I (B ).Thetypicalprobabilisticinformationmeasureis I (A)= log P (A).Thisistheappropriateconceptofinformationmeasurein supportofasubsetof Θ (ahypothesis).Now,considerthesetfunction I (Ho )= P (Tn ≥ t|Ho )on2Θ .Let Ho ⊇ Ho .IfweuseP-valuestorejectnullhypotheses ornot,e.g.,rejecting Ho (i.e.,thetrue θo / ∈ Ho )when,say, I (Ho ) ≤ α =0.05, thensince Ho ⊇ Ho ,wealsoreject Ho ,sothat I (Ho ) ≤ α,implyingthat Ho ⊇ Ho =⇒ I (Ho ) ≥ I (Ho )whichindicatesthat I (.)isnotaninformationmeasure (derivedfromempiricalevidence/data)insupportofhypotheses,sinceitisan increasingratherthanadecreasingsetfunction. P-valuesarenotmeasuresof strengthofevidence.
6H.T.Nguyen
4AreNeyman-PearsonTestingTheoryAffected?
SofarwehavejusttalkedaboutNHST.HowNeyman-Pearson(NP)testing frameworkdiffersfromNHST?Ofcourse,theyare“different”,butnow,inview ofthebanofP-valuesinNHST,you“love”toknowifthatban“affects”your routinetestingproblemswhereinteachingandresearch,infact,youareusing NPtestsinstead?Clearlythefindingsareextremelyimportant:eitheryoucan continuetoproceedwithallyourfamiliar(asymptotic)testssuchas Z -test, t-test, X 2 -test,KS-test,DF-test,....or...youarefacing“thefinalcollapseof theNeyman-Pearsondecisiontheoreticframework”(asannouncedbyHurlbert andLombardi[15]!Andinthelatter(!),areyoupanic?
InaccusingFisher’sworkonNHSTas“worsethanuseless”,Neymanand PearsonembarkedonshapingFisher’stestingsettingintoadecisionframework asweallknowandusesofar,althoughscienceisaboutdiscoveryofknowledge, andnotaboutdecision-making.The“improved”frameworkisthis.Besidesa hypothesis,denotedas Ho (althoughitisnotfornullifying,butinfactforacceptance),thereisaspecifiedalternativehypothesis Ha (tochooseif Ho happensto berejected).Itisamodelselectionproblem,whereeachhypothesiscorresponds toastatisticalmodel.TheNPtestingisadecision-makingproblem:usingdata torejectoraccept Ho .Bydoingso,twotypesoferrorsmightbecommitted: falsepositive: α = P (reject Ho |Ho istrue),falsenegative β = P (accept Ho |Ho isfalse).It“improves”uponFisher’sarbitrarychoiceofastatistictocompute theP-valuetoreachadecision,namelyamostpowerful“test”atafixed α-level. Notethatwhilethevalueof α couldbethesameinbothapproaches,say0.05 (a“small”numberin[0, 1]forFisher),itsmeaningisdifferent,as α =5%in NPapproach(theprobabilityofmakingthewrongdecisionofthefirstkind).
Let’sseehowNP carryout theirtests?Asatestisusuallybasedonsome appropriatestatistic Tn (X1 ,X2 ,...,Xn )(thoughtechnicallynotrequired)where, say, X1 ,X2 ,...,Xn isarandomsample,ofsize n,drawnfromthepopulation,so thatweselectaset B inthesamplespaceof Tn asarejection(critical)region.
Themostimportantquestionis :Whatisthe rationale forselectingaset B asarejectionregion?Sincedata(valuesofthestatistics Tn )in B leadto rejectionof Ho (i.e.,onthebasisofelementsof B wereject Ho ),this inference procedure hastohavea“plausible”explanationforpeopletotrust!Notethatan inferenceprocedureisnotamathematicaltheorem!Inotherwords,whyadata in B providesevidencetoreject Ho ?Clearly,thishassomethingtodowiththe statistic Tn (X1 ,X2 ,...,Xn )!
Given α anda(test)statistic Tn ,therejectionregion Rα isdeterminedby P (Tn ∈ Rα |Ho ) ≤ α
AreP-valuesleftoutinthisdeterminationofrejectionregions?(i.e.,the rationaleofinferenceinNPtestsdoesnotdependonP-valuesof Tn ?).Putit differently:Howto“pick”aregion Rα tobearejectionregion?
NotethattheP-valuestatistic p(Tn )=1 FTn |Ho (Tn )correspondstoaN-P test.Indeed,let α begivenasthetype-Ierror.Then,thetest,say, Sn ,which
OnEvidentialMeasuresofSupportforReasoning7
