Preface xiii
List of Contributors xv
Part I Kanti Mardia 1
1 A Conversation with Kanti Mardia 3
Nitis Mukhopadhyay
1.1 Family background 4
1.2 School days 6
1.3 College life 7
1.4 Ismail Yusuf College —University of Bombay 8
1.5 University of Bombay 10
1.6 A taste of the real world 12
1.7 Changes in the air 13
1.8 University of Rajasthan 14
1.9 Commonwealth scholarship to England 15
1.10 University of Newcastle 16
1.11 University of Hull 18
1.12 Book writing at the University of Hull 20
1.13 Directional data analysis 21
1.14 Chair Professorship of Applied Statistics, University of Leeds 25
1.15 Leeds annual workshops and conferences 28
1.16 High profile research areas 31
1.16.1 Multivariate analysis 32
1.16.2 Directional data 33
1.16.3 Shape analysis 34
1.16.4 Spatial statistics 36
1.16.5 Applied research 37
1.17 Center of Medical Imaging Research (CoMIR) 40
1.18 Visiting other places 41
1.19 Collaborators, colleagues and personalities 44
1.20 Logic, statistics and Jain religion 48
1.21 Many hobbies 50
1.22 Immediate family 51
1.23 Retirement 2000 53
Acknowledgments 55
References 55
2 A Conversation with Kanti Mardia: Part II 59
Nitis Mukhopadhyay
2.1 Introduction 59
2.2 Leeds, Oxford, and other affiliations 60
2.3 Book writing: revising and new ones 61
2.4 Research: bioinformatics and protein structure 63
2.5 Research: not necessarily linked directly with bioinformatics 66
2.6 Organizing centers and conferences 68
2.7 Memorable conference trips 71
2.8 A select group of special colleagues 73
2.9 High honors 74
2.10 Statistical science: thoughts and predictions 76
2.11 Immediate family 78
2.12 Jain thinking 80
2.13 What the future may hold 81
Acknowledgment 84
References 84
3 Selected publications 86
K V Mardia
Part II Directional Data Analysis 95
4 Some advances in constrained inference for ordered circular parameters in oscillatory systems 97
Cristina Rueda, Miguel A. Fernández, Sandra Barragán and Shyamal D. Peddada
4.1 Introduction 97
4.2 Oscillatory data and the problems of interest 99
4.3 Estimation of angular parameters under order constraint 101
4.4 Inferences under circular restrictions in von Mises models 103
4.5 The estimation of a common circular order from multiple experiments 105
4.6 Application: analysis of cell cycle gene expression data 107
4.7 Concluding remarks and future research 111
Acknowledgment 111
References 112
5 Parametric circular–circular regression and diagnostic analysis 115
Orathai Polsen and Charles C. Taylor
5.1 Introduction 115
5.2 Review of models 116
5.3 Parameter estimation and inference 118
5.4 Diagnostic analysis 119
5.4.1 Goodness-of-fit test for the von Mises distribution 120
5.4.2 Influential observations 121
5.5 Examples 123
5.6 Discussion 126
References 127
6 On two-sample tests for circular data based on spacing-frequencies 129
Riccardo Gatto and S. Rao Jammalamadaka
6.1 Introduction 129
6.2 Spacing-frequencies tests for circular data 130
6.2.1 Invariance, maximality and symmetries 131
6.2.2 An invariant class of spacing-frequencies tests 134
6.2.3 Multispacing-frequencies tests 136
6.2.4 Conditional representation and computation of the null distribution 137
6.3 Rao’s spacing-frequencies test for circular data 138
6.3.1 Rao’s test statistic and a geometric interpretation 139
6.3.2 Exact distribution 139
6.3.3 Saddlepoint approximation 140
6.4 Monte Carlo power comparisons 141
Acknowledgments 144
References 144
7 Barycentres and hurricane trajectories 146
Wilfrid S. Kendall
7.1 Introduction 146
7.2 Barycentres 147
7.3 Hurricanes 149
7.4 Using k-means and non-parametric statistics 151
7.5 Results 155
7.6 Conclusion 158
Acknowledgment 159
References 159
Part III Shape Analysis 161
8 Beyond Procrustes: a proposal to save morphometrics for biology 163
Fred L. Bookstein
8.1 Introduction 163
8.2 Analytic preliminaries 165
8.3 The core maneuver 168
8.4 Two examples 173
8.5 Some final thoughts 178
8.6 Summary 180
Acknowledgments 180
References 180
9 Nonparametric data analysis methods in medical imaging 182
Daniel E. Osborne, Vic Patrangenaru, Mingfei Qiu and Hilary W. Thompson
9.1 Introduction 182
9.2 Shape analysis of the optic nerve head 183
9.3 Extraction of 3D data from CT scans 187
9.3.1 CT data acquisition 187
9.3.2 Object extraction 189
9.4 Means on manifolds 190
9.4.1 Consistency of the Fre´chet sample mean 190
9.4.2 Nonparametric bootstrap 192
9.5 3D size-and-reflection shape manifold 193
9.5.1 Description of SRΣk 3,0 193
9.5.2 Schoenberg embeddings of SRΣk 3,0 193
9.5.3 Schoenberg extrinsic mean on SRΣk 3,0 194
9.6 3D size-and-reflection shape analysis of the human skull 194
9.6.1 Confidence regions for 3D mean size-and-reflection shape landmark configurations 194
9.7 DTI data analysis 196
9.8 MRI data analysis of corpus callosum image 200
Acknowledgments 203
References 203
10 Some families of distributions on higher shape spaces 206
Yasuko Chikuse and Peter E. Jupp
10.1 Introduction 206
10.1.1 Distributions on shape spaces 207
10.2 Shape distributions of angular central Gaussian type 209
10.2.1 Determinantal shape ACG distributions 209
10.2.2 Modified determinantal shape ACG distributions 211
10.2.3 Tracial shape ACG distributions 212
10.3 Distributions without reflective symmetry 213
10.3.1 Volume Fisher–Bingham distributions 213
10.3.2 Cardioid-type distributions 215
10.4 A test of reflective symmetry 215
10.5 Appendix: derivation of normalising constants 216
References 216
11 Elastic registration and shape analysis of functional objects 218
Zhengwu Zhang, Qian Xie, and Anuj Srivastava
11.1 Introduction 218
11.1.1 From discrete to continuous and elastic 219
11.1.2 General elastic framework 220
11.2 Registration in FDA: phase-amplitude separation 221
11.3 Elastic shape analysis of curves 223
11.3.1 Mean shape and modes of variations 225
11.3.2 Statistical shape models 226
11.4 Elastic shape analysis of surfaces 228
11.5 Metric-based image registration 231
11.6 Summary and future work 235
References 235
Part IV Spatial, Image and Multivariate Analysis 239
12 Evaluation of diagnostics for hierarchical spatial statistical models 241
Noel Cressie and Sandy Burden
12.1 Introduction 241
12.1.1 Hierarchical spatial statistical models 242
12.1.2 Diagnostics 242
12.1.3 Evaluation 243
12.2 Example: Sudden Infant Death Syndrome (SIDS) data for North C
OBNB doesn't sell books, but you may be able to find a copy at one of these websites:
Geometry Driven Statistics. ISBN 9781118866603. Published by Wiley in 2015. Publication and catalogue information, links to buy online and reader comments.
