spm使用的培训课件14Klaas-DCM-AdvancedTopics

DCM:AdvancedtopicsKlaasEnnoStephanLaboratoryforSocial&NeuralSystemsResearchInstituteforEmpiricalResearchinEconomicsUniversityofZurichWellcomeTrustCentreforNeuroimagingInstituteofNeurologyUniversityCollegeLondonSPMCourse2010UniversityofZurich,17-19February2010010203040506070809010000.10.20.30.4010203040506070809010000.20.40.6010203040506070809010000.10.20.3Neuralpopulationactivity010203040506070809010001230102030405060708090100-10123401020304050607080901000123fMRIsignalchange(%)010203040506070809010000.10.20.30.4010203040506070809010000.20.40.6010203040506070809010000.10.20.3Neuralpopulationactivity010203040506070809010001230102030405060708090100-10123401020304050607080901000123fMRIsignalchange(%)010203040506070809010001230102030405060708090100-10123401020304050607080901000123fMRIsignalchange(%)x1x2x3x1x2x3CuxDxBuAdtdxnjjjmiii1)(1)(u1u2),,(uxFdtdxNeuralstateequation:Electromagneticforwardmodel:neuralactivityEEGMEGLFPDynamicCausalModeling(DCM)simpleneuronalmodelcomplicatedforwardmodelcomplicatedneuronalmodelsimpleforwardmodelfMRIEEG/MEGinputsHemodynamicforwardmodel:neuralactivityBOLDOverview•Bayesianmodelselection(BMS)•NonlinearDCMforfMRI•EmbeddingcomputationalmodelsinDCMs•IntegratingtractographyandDCMModelcomparisonandselectionGivencompetinghypothesesonstructure&functionalmechanismsofasystem,whichmodelisthebest?Forwhichmodelmdoesp(y|m)becomemaximal?Whichmodelrepresentsthebestbalancebetweenmodelfitandmodelcomplexity?Pitt&Miyung(2002)TICSmypqKLmpqKLmypdmpmypmyp,|,|,),|(log)|(),|()|(Modelevidence:Variousapproximations,e.g.:-negativefreeenergy,AIC,BICBayesianmodelselection(BMS)accountsforbothaccuracyandcomplexityofthemodelallowsforinferenceaboutstructure(generalisability)ofthemodelallpossibledatasetsyp(y|m)Gharamani,2004McKay1992,NeuralComput.Pennyetal.2004,NeuroImageStephanetal.2007,NeuroImagepmypAIC),|(logLogarithmisamonotonicfunctionMaximizinglogmodelevidence=Maximizingmodelevidence)(),|(log)()()|(logmcomplexitymypmcomplexitymaccuracymypInSPM2&SPM5,interfaceoffers2approximations:NpmypBIClog2),|(logAkaikeInformationCriterion:BayesianInformationCriterion:Logmodelevidence=balancebetweenfitandcomplexityPennyetal.2004,NeuroImageApproximationstothemodelevidenceinDCMNo.ofparametersNo.ofdatapointsAICfavoursmorecomplexmodels,BICfavourssimplermodels.Thenegativefreeenergyapproximation•UnderGaussianassumptionsabouttheposterior(Laplaceapproximation),thenegativefreeenergyFisalowerboundonthelogmodelevidence:mypqKLFmypqKLmpqKLmypmyp,|,,|,|,),|(log)|(logmypqKLmypF,|,)|(logThecomplexityterminF•IncontrasttoAIC&BIC,thecomplexitytermofthenegativefreeenergyFaccountsforparameterinterdependencies.•ThecomplexitytermofFishigher–themoreindependentthepriorparameters(effectiveDFs)–themoredependenttheposteriorparameters–themoretheposteriormeandeviatesfromthepriormean•NB:SPM8onlyusesFformodelselection!yTyyCCCmpqKL|1||21ln21ln21)|(),(Bayesfactors)|()|(2112mypmypBpositivevalue,[0;[But:thelogevidenceisjustsomenumber–notveryintuitive!AmoreintuitiveinterpretationofmodelcomparisonsismadepossiblebyBayesfactors:Tocomparetwomodels,wecouldjustcomparetheirlogevidences.B12p(m1|y)Evidence1to350-75%weak3to2075-95%positive20to15095-99%strong15099%VerystrongKass&Rafteryclassification:Kass&Raftery1995,J.Am.Stat.Assoc.V1V5stimPPCM2attentionV1V5stimPPCM1attentionV1V5stimPPCM3attentionV1V5stimPPCM4attentionBF2966F=7.995M2betterthanM1BF12F=2.450M3betterthanM2BF23F=3.144M4betterthanM3M1M2M3M4BMSinSPM8:anexampleFixedeffectsBMSatgrouplevelGroupBayesfactor(GBF)for1...Ksubjects:AverageBayesfactor(ABF):Problems:-blindwithregardtogroupheterogeneity-sensitivetooutlierskkijijBFGBF)(()kKijijkABFBF)|(~111mypy)|(~111mypy)|(~222mypy)|(~111mypy)|(~pmpmkk);(~rDirr)|(~pmpmkk)|(~pmpmkk),1;(~1rmMultmRandomeffectsBMSforgroupstudiesDirichletparameters=“occurrences”ofmodelsinthepopulationDirichletdistributionofmodelprobabilitiesMultinomialdistributionofmodellabelsMeasureddatayModelinversionbyVariationalBayes(VB)Stephanetal.2009,NeuroImageIstheredletterleftorrightfromthemidlineoftheword?groupanalysis(randomeffects),n=16,p0.05correctedanalysiswithSPM2Task-drivenlateralisationletterdecisionsspatialdecisions•••DoesthewordcontaintheletterAornot?spatialdecisionsletterdecisionsStephanetal.2003,ScienceTheoriesoninter-hemisphericintegrationduringlateralisedtasksInformationtransfer(forleft-lateralisedtask)Inhibition/CompetitionHemisphericrecruitmentLVFRVFTTTT+−−TT++Predictions:modulationbytaskconditionalonvisualfieldasymmetricconnectionstrengthsPredictions:modulationbytaskonlynegative&symmetricconnectionstrengthsPredictions:modulationbytaskonlypositive&symmetricconnectionstrengths|LVF|RVFLGleftLGrightFGrightFGleftRVFLVFBABcondBindLDVFVFLDBindBcondintrainter16modelsLGleftLGrightFGrightFGleftLDRVFLVFLGleftLGrightRVFstim.LVFstim.FGrightFGleftLDLD,RVFLD|RVFLDLD,LVFLD|LVFVFLDBindBcondLDRVFLVFLD|RVFLD|LVFVFLDBindBcondDCLGleftLGrightRVFstim.LVFstim.FGrig