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A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia
This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia's work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field.
Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.
List of contents
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
About the author
Ian L. Dryden, University of Nottingham, UK
John T. Kent, University of Leeds, UK
Summary
A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia's long and influential career in statistics.
