Geometry driven statistics

416 Pages·2015·17.432 MB·English

by  Dryden, Ian L., Kent, John T

Geometry Driven Statistics
Geometry Driven Statistics
Editedby
Ian L. Dryden
UniversityofNottingham, UK
John T. Kent
UniversityofLeeds,UK
Thiseditionfirstpublished2015
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1 2015
Contents
Preface xiii
ListofContributors xv
PartI KantiMardia 1
1 AConversationwithKantiMardia 3
NitisMukhopadhyay
1.1 Familybackground 4
1.2 Schooldays 6
1.3 Collegelife 7
1.4 IsmailYusufCollege—UniversityofBombay 8
1.5 UniversityofBombay 10
1.6 Atasteoftherealworld 12
1.7 Changesintheair 13
1.8 UniversityofRajasthan 14
1.9 CommonwealthscholarshiptoEngland 15
1.10 UniversityofNewcastle 16
1.11 UniversityofHull 18
1.12 BookwritingattheUniversityofHull 20
1.13 Directionaldataanalysis 21
1.14 ChairProfessorshipofAppliedStatistics,UniversityofLeeds 25
1.15 Leedsannualworkshopsandconferences 28
1.16 Highprofileresearchareas 31
1.16.1 Multivariateanalysis 32
1.16.2 Directionaldata 33
1.16.3 Shapeanalysis 34
1.16.4 Spatialstatistics 36
1.16.5 Appliedresearch 37
1.17 CenterofMedicalImagingResearch(CoMIR) 40
vi CONTENTS
1.18 Visitingotherplaces 41
1.19 Collaborators,colleaguesandpersonalities 44
1.20 Logic,statisticsandJainreligion 48
1.21 Manyhobbies 50
1.22 Immediatefamily 51
1.23 Retirement2000 53
Acknowledgments 55
References 55
2 AConversationwithKantiMardia:PartII 59
NitisMukhopadhyay
2.1 Introduction 59
2.2 Leeds,Oxford,andotheraffiliations 60
2.3 Bookwriting:revisingandnewones 61
2.4 Research:bioinformaticsandproteinstructure 63
2.5 Research:notnecessarilylinkeddirectlywithbioinformatics 66
2.6 Organizingcentersandconferences 68
2.7 Memorableconferencetrips 71
2.8 Aselectgroupofspecialcolleagues 73
2.9 Highhonors 74
2.10 Statisticalscience:thoughtsandpredictions 76
2.11 Immediatefamily 78
2.12 Jainthinking 80
2.13 Whatthefuturemayhold 81
Acknowledgment 84
References 84
3 Selectedpublications 86
KVMardia
PartII DirectionalDataAnalysis 95
4 Someadvancesinconstrainedinferencefororderedcircularparameters
inoscillatorysystems 97
CristinaRueda,MiguelA.Fernández,SandraBarragánand
ShyamalD.Peddada
4.1 Introduction 97
4.2 Oscillatorydataandtheproblemsofinterest 99
4.3 Estimationofangularparametersunderorderconstraint 101
4.4 InferencesundercircularrestrictionsinvonMisesmodels 103
4.5 Theestimationofacommoncircularorderfrommultipleexperiments 105
4.6 Application:analysisofcellcyclegeneexpressiondata 107
4.7 Concludingremarksandfutureresearch 111
Acknowledgment 111
References 112
CONTENTS vii
5 Parametriccircular–circularregressionanddiagnosticanalysis 115
OrathaiPolsenandCharlesC.Taylor
5.1 Introduction 115
5.2 Reviewofmodels 116
5.3 Parameterestimationandinference 118
5.4 Diagnosticanalysis 119
5.4.1 Goodness-of-fittestforthevonMisesdistribution 120
5.4.2 Influentialobservations 121
5.5 Examples 123
5.6 Discussion 126
References 127
6 Ontwo-sampletestsforcirculardatabasedonspacing-frequencies 129
RiccardoGattoandS.RaoJammalamadaka
6.1 Introduction 129
6.2 Spacing-frequenciestestsforcirculardata 130
6.2.1 Invariance,maximalityandsymmetries 131
6.2.2 Aninvariantclassofspacing-frequenciestests 134
6.2.3 Multispacing-frequenciestests 136
6.2.4 Conditionalrepresentationandcomputationofthenull
distribution 137
6.3 Rao’sspacing-frequenciestestforcirculardata 138
6.3.1 Rao’steststatisticandageometricinterpretation 139
6.3.2 Exactdistribution 139
6.3.3 Saddlepointapproximation 140
6.4 MonteCarlopowercomparisons 141
Acknowledgments 144
References 144
7 Barycentresandhurricanetrajectories 146
WilfridS.Kendall
7.1 Introduction 146
7.2 Barycentres 147
7.3 Hurricanes 149
7.4 Usingk-meansandnon-parametricstatistics 151
7.5 Results 155
7.6 Conclusion 158
Acknowledgment 159
References 159
PartIII ShapeAnalysis 161
8 BeyondProcrustes:aproposaltosavemorphometricsforbiology 163
FredL.Bookstein
8.1 Introduction 163
viii CONTENTS
8.2 Analyticpreliminaries 165
8.3 Thecoremaneuver 168
8.4 Twoexamples 173
8.5 Somefinalthoughts 178
8.6 Summary 180
Acknowledgments 180
References 180
9 Nonparametricdataanalysismethodsinmedicalimaging 182
DanielE.Osborne,VicPatrangenaru,MingfeiQiuandHilaryW.Thompson
9.1 Introduction 182
9.2 Shapeanalysisoftheopticnervehead 183
9.3 Extractionof3DdatafromCTscans 187
9.3.1 CTdataacquisition 187
9.3.2 Objectextraction 189
9.4 Meansonmanifolds 190
9.4.1 ConsistencyoftheFrec´hetsamplemean 190
9.4.2 Nonparametricbootstrap 192
9.5 3Dsize-and-reflectionshapemanifold 193
9.5.1 DescriptionofSRΣk 193
3,0
9.5.2 SchoenbergembeddingsofSRΣk 193
3,0
9.5.3 SchoenbergextrinsicmeanonSRΣk 194
3,0
9.6 3Dsize-and-reflectionshapeanalysisofthehumanskull 194
9.6.1 Confidence regions for 3D mean size-and-reflection shape
landmarkconfigurations 194
9.7 DTIdataanalysis 196
9.8 MRIdataanalysisofcorpuscallosumimage 200
Acknowledgments 203
References 203
10 Somefamiliesofdistributionsonhighershapespaces 206
YasukoChikuseandPeterE.Jupp
10.1 Introduction 206
10.1.1 Distributionsonshapespaces 207
10.2 ShapedistributionsofangularcentralGaussiantype 209
10.2.1 DeterminantalshapeACGdistributions 209
10.2.2 ModifieddeterminantalshapeACGdistributions 211
10.2.3 TracialshapeACGdistributions 212
10.3 Distributionswithoutreflectivesymmetry 213
10.3.1 VolumeFisher–Binghamdistributions 213
10.3.2 Cardioid-typedistributions 215
10.4 Atestofreflectivesymmetry 215
10.5 Appendix:derivationofnormalisingconstants 216
References 216
11 Elasticregistrationandshapeanalysisoffunctionalobjects 218
ZhengwuZhang,QianXie,andAnujSrivastava
11.1 Introduction 218
CONTENTS ix
11.1.1 Fromdiscretetocontinuousandelastic 219
11.1.2 Generalelasticframework 220
11.2 RegistrationinFDA:phase-amplitudeseparation 221
11.3 Elasticshapeanalysisofcurves 223
11.3.1 Meanshapeandmodesofvariations 225
11.3.2 Statisticalshapemodels 226
11.4 Elasticshapeanalysisofsurfaces 228
11.5 Metric-basedimageregistration 231
11.6 Summaryandfuturework 235
References 235
PartIV Spatial,ImageandMultivariateAnalysis 239
12 Evaluationofdiagnosticsforhierarchicalspatialstatisticalmodels 241
NoelCressieandSandyBurden
12.1 Introduction 241
12.1.1 Hierarchicalspatialstatisticalmodels 242
12.1.2 Diagnostics 242
12.1.3 Evaluation 243
12.2 Example: Sudden Infant Death Syndrome (SIDS) data for North
Carolina 244
12.3 Diagnosticsasinstrumentsofdiscovery 247
12.3.1 Nonhierarchicalspatialmodel 250
12.3.2 Hierarchicalspatialmodel 251
12.4 Evaluationofdiagnostics 252
12.4.1 DSCcurvesfornonhierarchicalspatialmodels 253
12.4.2 DSCcurvesforhierarchicalspatialmodels 254
12.5 Discussionandconclusions 254
Acknowledgments 254
References 255
13 Bayesianforecastingusingspatiotemporalmodelswithapplications
toozoneconcentrationlevelsintheEasternUnitedStates 260
SujitKumarSahu,KhandokerShuvoBakarandNorhashidahAwang
13.1 Introduction 260
13.2 Testdataset 262
13.3 Forecastingmethods 264
13.3.1 Preliminaries 264
13.3.2 ForecastingusingGPmodels 265
13.3.3 ForecastingusingARmodels 267
13.3.4 ForecastingusingtheGPPmodels 268
13.4 Forecastcalibrationmethods 269
13.5 Resultsfromasmallerdataset 272
13.6 AnalysisofthefullEasternUSdataset 276
13.7 Conclusion 278
References 279
x CONTENTS
14 Visualisation 282
JohnC.Gower
14.1 Introduction 282
14.2 Theproblem 284
14.3 Apossiblesolution:self-explanatoryvisualisations 286
References 287
15 Fingerprintimageanalysis:roleoforientationpatchandridgestructure
dictionaries 288
AnilK.JainandKaiCao
15.1 Introduction 288
15.2 Dictionaryconstruction 292
15.2.1 Orientationpatchdictionaryconstruction 292
15.2.2 Ridgestructuredictionaryconstruction 293
15.3 Orientationfieldestimationusingorientationpatchdictionary 296
15.3.1 Initialorientationfieldestimation 296
15.3.2 Dictionarylookup 297
15.3.3 Context-basedorientationfieldcorrection 297
15.3.4 Experiments 298
15.4 Latentsegmentationandenhancementusingridgestructuredictionary 301
15.4.1 Latentimagedecomposition 302
15.4.2 Coarseestimatesofridgequality,orientation,andfrequency 303
15.4.3 Fineestimatesofridgequality,orientation,andfrequency 305
15.4.4 Segmentationandenhancement 305
15.4.5 Experimentalresults 305
15.5 Conclusionsandfuturework 307
References 307
PartV Bioinformatics 311
16 Doproteinstructuresevolvearound‘anchor’residues? 313
ColleenNooney,AriefGusnanto,WalterR.GilksandStuartBarber
16.1 Introduction 313
16.1.1 Overview 313
16.1.2 Proteinsequencesandstructures 314
16.2 Exploratorydataanalysis 315
16.2.1 Trypsinproteinfamily 315
16.2.2 Multiplestructurealignment 316
16.2.3 Aligneddistancematrixanalysis 317
16.2.4 Mediandistancematrixanalysis 319
16.2.5 Divergencedistancematrixanalysis 320
16.3 Aretheanchorresiduesartefacts? 325
16.3.1 Aligninganotherproteinfamily 325
16.3.2 Aligninganartificialsampleoftrypsinstructures 325
16.3.3 AligningC atomsoftherealtrypsinsample 329
α
16.3.4 Aligning the real trypsin sample with anchor residues
removed 330
CONTENTS xi
16.4 Effectofgap-closingmethodonstructureshape 331
16.4.1 Zig-zag 331
16.4.2 Idealisedhelix 331
16.5 Alternativetomultiplestructurealignment 332
16.6 Discussion 334
References 335
17 Individualiseddivergences 337
CliveE.Bowman
17.1 Thepast:genealogyofdivergencesandthemanofAneka¯ntava¯da 337
17.2 Thepresent:divergencesandprofileshape 338
17.2.1 Notation 338
17.2.2 Knownparameters 339
17.2.3 Thelikelihoodformulation 342
17.2.4 Dealingwithmultivariatedata–theoverallalgorithm 343
17.2.5 Briefnewexample 345
17.2.6 Justificationfortheconsiderationofindividualised
divergences 347
17.3 Thefuture:challengingdata 348
17.3.1 Contrastsofmorethantwogroups 348
17.3.2 Otherdatadistributions 351
17.3.3 Othermethods 352
References 353
18 Proteins,physicsandprobabilitykinematics:aBayesianformulationof
theproteinfoldingproblem 356
ThomasHamelryck,WouterBoomsma,JesperFerkinghoff-Borg,Jesper
Foldager,JesFrellsen,JohnHaslettandDouglasTheobald
18.1 Introduction 356
18.2 Overviewofthearticle 359
18.3 Probabilisticformulation 360
18.4 Localandnon-localstructure 360
18.5 Thelocalmodel 362
18.6 Thenon-localmodel 363
18.7 Theformulationofthejointmodel 364
18.7.1 Outlineoftheproblemanditssolution 364
18.7.2 Modelcombinationexplanation 365
18.7.3 Conditionalindependenceexplanation 366
18.7.4 Marginalizationexplanation 366
18.7.5 Jacobianexplanation 367
18.7.6 Equivalenceoftheindependenceassumptions 367
18.7.7 Probabilitykinematicsexplanation 368
18.7.8 Bayesianexplanation 369
18.8 Kullback–Leibleroptimality 370
18.9 Linkwithstatisticalpotentials 371
18.10 Conclusionsandoutlook 372
Acknowledgments 373
References 373