{"product_id":"geometry-driven-statistics-isbn-9781118866573","title":"Geometry Driven Statistics","description":"\u003cp\u003e\u003cb\u003eA 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\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eGeometry Driven Statistics\u003c\/i\u003e 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.\u003c\/p\u003e Summarizing the state of the art, examining some new developments and presenting a vision for the future, \u003ci\u003eGeometry Driven Statistics\u003c\/i\u003e 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. \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eList of Contributors xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Kanti Mardia 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 A Conversation with Kanti Mardia 3\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eNitis Mukhopadhyay\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Family background 4\u003c\/p\u003e \u003cp\u003e1.2 School days 6\u003c\/p\u003e \u003cp\u003e1.3 College life 7\u003c\/p\u003e \u003cp\u003e1.4 Ismail Yusuf College — University of Bombay 8\u003c\/p\u003e \u003cp\u003e1.5 University of Bombay 10\u003c\/p\u003e \u003cp\u003e1.6 A taste of the real world 12\u003c\/p\u003e \u003cp\u003e1.7 Changes in the air 13\u003c\/p\u003e \u003cp\u003e1.8 University of Rajasthan 14\u003c\/p\u003e \u003cp\u003e1.9 Commonwealth scholarship to England 15\u003c\/p\u003e \u003cp\u003e1.10 University of Newcastle 16\u003c\/p\u003e \u003cp\u003e1.11 University of Hull 18\u003c\/p\u003e \u003cp\u003e1.12 Book writing at the University of Hull 20\u003c\/p\u003e \u003cp\u003e1.13 Directional data analysis 21\u003c\/p\u003e \u003cp\u003e1.14 Chair Professorship of Applied Statistics, University of Leeds 25\u003c\/p\u003e \u003cp\u003e1.15 Leeds annual workshops and conferences 28\u003c\/p\u003e \u003cp\u003e1.16 High profile research areas 31\u003c\/p\u003e \u003cp\u003e1.16.1 Multivariate analysis 32\u003c\/p\u003e \u003cp\u003e1.16.2 Directional data 33\u003c\/p\u003e \u003cp\u003e1.16.3 Shape analysis 34\u003c\/p\u003e \u003cp\u003e1.16.4 Spatial statistics 36\u003c\/p\u003e \u003cp\u003e1.16.5 Applied research 37\u003c\/p\u003e \u003cp\u003e1.17 Center of Medical Imaging Research (CoMIR) 40\u003c\/p\u003e \u003cp\u003e1.18 Visiting other places 41\u003c\/p\u003e \u003cp\u003e1.19 Collaborators, colleagues and personalities 44\u003c\/p\u003e \u003cp\u003e1.20 Logic, statistics and Jain religion 48\u003c\/p\u003e \u003cp\u003e1.21 Many hobbies 50\u003c\/p\u003e \u003cp\u003e1.22 Immediate family 51\u003c\/p\u003e \u003cp\u003e1.23 Retirement 2000 53\u003c\/p\u003e \u003cp\u003eAcknowledgments 55\u003c\/p\u003e \u003cp\u003eReferences 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 a Conversation with Kanti Mardia: Part II 59\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eNitis Mukhopadhyay\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 59\u003c\/p\u003e \u003cp\u003e2.2 Leeds, Oxford, and other affiliations 60\u003c\/p\u003e \u003cp\u003e2.3 Book writing: revising and new ones 61\u003c\/p\u003e \u003cp\u003e2.4 Research: bioinformatics and protein structure 63\u003c\/p\u003e \u003cp\u003e2.5 Research: not necessarily linked directly with bioinformatics 66\u003c\/p\u003e \u003cp\u003e2.6 Organizing centers and conferences 68\u003c\/p\u003e \u003cp\u003e2.7 Memorable conference trips 71\u003c\/p\u003e \u003cp\u003e2.8 A select group of special colleagues 73\u003c\/p\u003e \u003cp\u003e2.9 High honors 74\u003c\/p\u003e \u003cp\u003e2.10 Statistical science: thoughts and predictions 76\u003c\/p\u003e \u003cp\u003e2.11 Immediate family 78\u003c\/p\u003e \u003cp\u003e2.12 Jain thinking 80\u003c\/p\u003e \u003cp\u003e2.13 What the future may hold 81\u003c\/p\u003e \u003cp\u003eAcknowledgment 84\u003c\/p\u003e \u003cp\u003eReferences 84\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Selected publications 86\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eK V Mardia\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Directional Data Analysis 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Some advances in constrained inference for ordered circular parameters in oscillatory systems 97\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eCristina Rueda, Miguel A. Fernández, Sandra Barragán and Shyamal D. Peddada\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 97\u003c\/p\u003e \u003cp\u003e4.2 Oscillatory data and the problems of interest 99\u003c\/p\u003e \u003cp\u003e4.3 Estimation of angular parameters under order constraint 101\u003c\/p\u003e \u003cp\u003e4.4 Inferences under circular restrictions in von Mises models 103\u003c\/p\u003e \u003cp\u003e4.5 The estimation of a common circular order from multiple experiments 105\u003c\/p\u003e \u003cp\u003e4.6 Application: analysis of cell cycle gene expression data 107\u003c\/p\u003e \u003cp\u003e4.7 Concluding remarks and future research 111\u003c\/p\u003e \u003cp\u003eAcknowledgment 111\u003c\/p\u003e \u003cp\u003eReferences 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Parametric circular–circular regression and diagnostic analysis 115\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eOrathai Polsen and Charles C. Taylor\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 115\u003c\/p\u003e \u003cp\u003e5.2 Review of models 116\u003c\/p\u003e \u003cp\u003e5.3 Parameter estimation and inference 118\u003c\/p\u003e \u003cp\u003e5.4 Diagnostic analysis 119\u003c\/p\u003e \u003cp\u003e5.4.1 Goodness-of-fit test for the von Mises distribution 120\u003c\/p\u003e \u003cp\u003e5.4.2 Influential observations 121\u003c\/p\u003e \u003cp\u003e5.5 Examples 123\u003c\/p\u003e \u003cp\u003e5.6 Discussion 126\u003c\/p\u003e \u003cp\u003eReferences 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 On two-sample tests for circular data based on spacing-frequencies 129\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eRiccardo Gatto and S. Rao Jammalamadaka\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 129\u003c\/p\u003e \u003cp\u003e6.2 Spacing-frequencies tests for circular data 130\u003c\/p\u003e \u003cp\u003e6.2.1 Invariance, maximality and symmetries 131\u003c\/p\u003e \u003cp\u003e6.2.2 An invariant class of spacing-frequencies tests 134\u003c\/p\u003e \u003cp\u003e6.2.3 Multispacing-frequencies tests 136\u003c\/p\u003e \u003cp\u003e6.2.4 Conditional representation and computation of the null distribution 137\u003c\/p\u003e \u003cp\u003e6.3 Rao’s spacing-frequencies test for circular data 138\u003c\/p\u003e \u003cp\u003e6.3.1 Rao’s test statistic and a geometric interpretation 139\u003c\/p\u003e \u003cp\u003e6.3.2 Exact distribution 139\u003c\/p\u003e \u003cp\u003e6.3.3 Saddlepoint approximation 140\u003c\/p\u003e \u003cp\u003e6.4 Monte Carlo power comparisons 141\u003c\/p\u003e \u003cp\u003eAcknowledgments 144\u003c\/p\u003e \u003cp\u003eReferences 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Barycentres and hurricane trajectories 146\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eWilfrid S. Kendall\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 146\u003c\/p\u003e \u003cp\u003e7.2 Barycentres 147\u003c\/p\u003e \u003cp\u003e7.3 Hurricanes 149\u003c\/p\u003e \u003cp\u003e7.4 Using k-means and non-parametric statistics 151\u003c\/p\u003e \u003cp\u003e7.5 Results 155\u003c\/p\u003e \u003cp\u003e7.6 Conclusion 158\u003c\/p\u003e \u003cp\u003eAcknowledgment 159\u003c\/p\u003e \u003cp\u003eReferences 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Shape Analysis 161\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Beyond Procrustes: a proposal to save morphometrics for biology 163\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eFred L. Bookstein\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 163\u003c\/p\u003e \u003cp\u003e8.2 Analytic preliminaries 165\u003c\/p\u003e \u003cp\u003e8.3 The core maneuver 168\u003c\/p\u003e \u003cp\u003e8.4 Two examples 173\u003c\/p\u003e \u003cp\u003e8.5 Some final thoughts 178\u003c\/p\u003e \u003cp\u003e8.6 Summary 180\u003c\/p\u003e \u003cp\u003eAcknowledgments 180\u003c\/p\u003e \u003cp\u003eReferences 180\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Nonparametric data analysis methods in medical imaging 182\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eDaniel E. Osborne, Vic Patrangenaru, Mingfei Qiu and Hilary W. Thompson\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 182\u003c\/p\u003e \u003cp\u003e9.2 Shape analysis of the optic nerve head 183\u003c\/p\u003e \u003cp\u003e9.3 Extraction of 3D data from CT scans 187\u003c\/p\u003e \u003cp\u003e9.3.1 CT data acquisition 187\u003c\/p\u003e \u003cp\u003e9.3.2 Object extraction 189\u003c\/p\u003e \u003cp\u003e9.4 Means on manifolds 190\u003c\/p\u003e \u003cp\u003e9.4.1 Consistency of the Frećhet sample mean 190\u003c\/p\u003e \u003cp\u003e9.4.2 Nonparametric bootstrap 192\u003c\/p\u003e \u003cp\u003e9.5 3D size-and-reflection shape manifold 193\u003c\/p\u003e \u003cp\u003e9.5.1 Description of SRΣ k 3,0 193\u003c\/p\u003e \u003cp\u003e9.5.2 Schoenberg embeddings of SRΣ k 3,0 193\u003c\/p\u003e \u003cp\u003e9.5.3 Schoenberg extrinsic mean on SRΣ k 3,0 194\u003c\/p\u003e \u003cp\u003e9.6 3D size-and-reflection shape analysis of the human skull 194\u003c\/p\u003e \u003cp\u003e9.6.1 Confidence regions for 3D mean size-and-reflection shape landmark configurations 194\u003c\/p\u003e \u003cp\u003e9.7 DTI data analysis 196\u003c\/p\u003e \u003cp\u003e9.8 MRI data analysis of corpus callosum image 200\u003c\/p\u003e \u003cp\u003eAcknowledgments 203\u003c\/p\u003e \u003cp\u003eReferences 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Some families of distributions on higher shape spaces 206\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eYasuko Chikuse and Peter E. Jupp\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 206\u003c\/p\u003e \u003cp\u003e10.1.1 Distributions on shape spaces 207\u003c\/p\u003e \u003cp\u003e10.2 Shape distributions of angular central Gaussian type 209\u003c\/p\u003e \u003cp\u003e10.2.1 Determinantal shape ACG distributions 209\u003c\/p\u003e \u003cp\u003e10.2.2 Modified determinantal shape ACG distributions 211\u003c\/p\u003e \u003cp\u003e10.2.3 Tracial shape ACG distributions 212\u003c\/p\u003e \u003cp\u003e10.3 Distributions without reflective symmetry 213\u003c\/p\u003e \u003cp\u003e10.3.1 Volume Fisher–Bingham distributions 213\u003c\/p\u003e \u003cp\u003e10.3.2 Cardioid-type distributions 215\u003c\/p\u003e \u003cp\u003e10.4 A test of reflective symmetry 215\u003c\/p\u003e \u003cp\u003e10.5 Appendix: derivation of normalising constants 216\u003c\/p\u003e \u003cp\u003eReferences 216\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Elastic registration and shape analysis of functional objects 218\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eZhengwu Zhang, Qian Xie, and Anuj Srivastava\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 218\u003c\/p\u003e \u003cp\u003e11.1.1 From discrete to continuous and elastic 219\u003c\/p\u003e \u003cp\u003e11.1.2 General elastic framework 220\u003c\/p\u003e \u003cp\u003e11.2 Registration in FDA: phase-amplitude separation 221\u003c\/p\u003e \u003cp\u003e11.3 Elastic shape analysis of curves 223\u003c\/p\u003e \u003cp\u003e11.3.1 Mean shape and modes of variations 225\u003c\/p\u003e \u003cp\u003e11.3.2 Statistical shape models 226\u003c\/p\u003e \u003cp\u003e11.4 Elastic shape analysis of surfaces 228\u003c\/p\u003e \u003cp\u003e11.5 Metric-based image registration 231\u003c\/p\u003e \u003cp\u003e11.6 Summary and future work 235\u003c\/p\u003e \u003cp\u003eReferences 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Spatial, Image and Multivariate Analysis 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Evaluation of diagnostics for hierarchical spatial statistical models 241\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eNoel Cressie and Sandy Burden\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 241\u003c\/p\u003e \u003cp\u003e12.1.1 Hierarchical spatial statistical models 242\u003c\/p\u003e \u003cp\u003e12.1.2 Diagnostics 242\u003c\/p\u003e \u003cp\u003e12.1.3 Evaluation 243\u003c\/p\u003e \u003cp\u003e12.2 Example: Sudden Infant Death Syndrome (SIDS) data for North Carolina 244\u003c\/p\u003e \u003cp\u003e12.3 Diagnostics as instruments of discovery 247\u003c\/p\u003e \u003cp\u003e12.3.1 Nonhierarchical spatial model 250\u003c\/p\u003e \u003cp\u003e12.3.2 Hierarchical spatial model 251\u003c\/p\u003e \u003cp\u003e12.4 Evaluation of diagnostics 252\u003c\/p\u003e \u003cp\u003e12.4.1 DSC curves for nonhierarchical spatial models 253\u003c\/p\u003e \u003cp\u003e12.4.2 DSC curves for hierarchical spatial models 254\u003c\/p\u003e \u003cp\u003e12.5 Discussion and conclusions 254\u003c\/p\u003e \u003cp\u003eAcknowledgments 254\u003c\/p\u003e \u003cp\u003eReferences 255\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Bayesian forecasting using spatiotemporal models with applications to ozone concentration levels in the Eastern United States 260\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eSujit Kumar Sahu, Khandoker Shuvo Bakar and Norhashidah Awang\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 260\u003c\/p\u003e \u003cp\u003e13.2 Test data set 262\u003c\/p\u003e \u003cp\u003e13.3 Forecasting methods 264\u003c\/p\u003e \u003cp\u003e13.3.1 Preliminaries 264\u003c\/p\u003e \u003cp\u003e13.3.2 Forecasting using GP models 265\u003c\/p\u003e \u003cp\u003e13.3.3 Forecasting using AR models 267\u003c\/p\u003e \u003cp\u003e13.3.4 Forecasting using the GPP models 268\u003c\/p\u003e \u003cp\u003e13.4 Forecast calibration methods 269\u003c\/p\u003e \u003cp\u003e13.5 Results from a smaller data set 272\u003c\/p\u003e \u003cp\u003e13.6 Analysis of the full Eastern US data set 276\u003c\/p\u003e \u003cp\u003e13.7 Conclusion 278\u003c\/p\u003e \u003cp\u003eReferences 279\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Visualisation 282\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eJohn C. Gower\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 282\u003c\/p\u003e \u003cp\u003e14.2 The problem 284\u003c\/p\u003e \u003cp\u003e14.3 A possible solution: self-explanatory visualisations 286\u003c\/p\u003e \u003cp\u003eReferences 287\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Fingerprint image analysis: role of orientation patch and ridge structure dictionaries 288\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eAnil K. Jain and Kai Cao\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 288\u003c\/p\u003e \u003cp\u003e15.2 Dictionary construction 292\u003c\/p\u003e \u003cp\u003e15.2.1 Orientation patch dictionary construction 292\u003c\/p\u003e \u003cp\u003e15.2.2 Ridge structure dictionary construction 293\u003c\/p\u003e \u003cp\u003e15.3 Orientation field estimation using orientation patch dictionary 296\u003c\/p\u003e \u003cp\u003e15.3.1 Initial orientation field estimation 296\u003c\/p\u003e \u003cp\u003e15.3.2 Dictionary lookup 297\u003c\/p\u003e \u003cp\u003e15.3.3 Context-based orientation field correction 297\u003c\/p\u003e \u003cp\u003e15.3.4 Experiments 298\u003c\/p\u003e \u003cp\u003e15.4 Latent segmentation and enhancement using ridge structure dictionary 301\u003c\/p\u003e \u003cp\u003e15.4.1 Latent image decomposition 302\u003c\/p\u003e \u003cp\u003e15.4.2 Coarse estimates of ridge quality, orientation, and frequency 303\u003c\/p\u003e \u003cp\u003e15.4.3 Fine estimates of ridge quality, orientation, and frequency 305\u003c\/p\u003e \u003cp\u003e15.4.4 Segmentation and enhancement 305\u003c\/p\u003e \u003cp\u003e15.4.5 Experimental results 305\u003c\/p\u003e \u003cp\u003e15.5 Conclusions and future work 307\u003c\/p\u003e \u003cp\u003eReferences 307\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Bioinformatics 311\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Do protein structures evolve around ‘anchor’ residues? 313\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eColleen Nooney, Arief Gusnanto, Walter R. Gilks and Stuart Barber\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 313\u003c\/p\u003e \u003cp\u003e16.1.1 Overview 313\u003c\/p\u003e \u003cp\u003e16.1.2 Protein sequences and structures 314\u003c\/p\u003e \u003cp\u003e16.2 Exploratory data analysis 315\u003c\/p\u003e \u003cp\u003e16.2.1 Trypsin protein family 315\u003c\/p\u003e \u003cp\u003e16.2.2 Multiple structure alignment 316\u003c\/p\u003e \u003cp\u003e16.2.3 Aligned distance matrix analysis 317\u003c\/p\u003e \u003cp\u003e16.2.4 Median distance matrix analysis 319\u003c\/p\u003e \u003cp\u003e16.2.5 Divergence distance matrix analysis 320\u003c\/p\u003e \u003cp\u003e16.3 Are the anchor residues artefacts? 325\u003c\/p\u003e \u003cp\u003e16.3.1 Aligning another protein family 325\u003c\/p\u003e \u003cp\u003e16.3.2 Aligning an artificial sample of trypsin structures 325\u003c\/p\u003e \u003cp\u003e16.3.3 Aligning C α atoms of the real trypsin sample 329\u003c\/p\u003e \u003cp\u003e16.3.4 Aligning the real trypsin sample with anchor residues removed 330\u003c\/p\u003e \u003cp\u003e16.4 Effect of gap-closing method on structure shape 331\u003c\/p\u003e \u003cp\u003e16.4.1 Zig-zag 331\u003c\/p\u003e \u003cp\u003e16.4.2 Idealised helix 331\u003c\/p\u003e \u003cp\u003e16.5 Alternative to multiple structure alignment 332\u003c\/p\u003e \u003cp\u003e16.6 Discussion 334\u003c\/p\u003e \u003cp\u003eReferences 335\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Individualised divergences 337\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eClive E. Bowman\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 The past: genealogy of divergences and the man of Anekāntavāda 337\u003c\/p\u003e \u003cp\u003e17.2 The present: divergences and profile shape 338\u003c\/p\u003e \u003cp\u003e17.2.1 Notation 338\u003c\/p\u003e \u003cp\u003e17.2.2 Known parameters 339\u003c\/p\u003e \u003cp\u003e17.2.3 The likelihood formulation 342\u003c\/p\u003e \u003cp\u003e17.2.4 Dealing with multivariate data – the overall algorithm 343\u003c\/p\u003e \u003cp\u003e17.2.5 Brief new example 345\u003c\/p\u003e \u003cp\u003e17.2.6 Justification for the consideration of individualised divergences 347\u003c\/p\u003e \u003cp\u003e17.3 The future: challenging data 348\u003c\/p\u003e \u003cp\u003e17.3.1 Contrasts of more than two groups 348\u003c\/p\u003e \u003cp\u003e17.3.2 Other data distributions 351\u003c\/p\u003e \u003cp\u003e17.3.3 Other methods 352\u003c\/p\u003e \u003cp\u003eReferences 353\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Proteins, physics and probability kinematics: a Bayesian formulation of the protein folding problem 356\u003cbr\u003e \u003c\/b\u003e\u003ci\u003eThomas Hamelryck, Wouter Boomsma, Jesper Ferkinghoff-Borg, Jesper Foldager, Jes Frellsen, John Haslett and Douglas Theobald\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 356\u003c\/p\u003e \u003cp\u003e18.2 Overview of the article 359\u003c\/p\u003e \u003cp\u003e18.3 Probabilistic formulation 360\u003c\/p\u003e \u003cp\u003e18.4 Local and non-local structure 360\u003c\/p\u003e \u003cp\u003e18.5 The local model 362\u003c\/p\u003e \u003cp\u003e18.6 The non-local model 363\u003c\/p\u003e \u003cp\u003e18.7 The formulation of the joint model 364\u003c\/p\u003e \u003cp\u003e18.7.1 Outline of the problem and its solution 364\u003c\/p\u003e \u003cp\u003e18.7.2 Model combination explanation 365\u003c\/p\u003e \u003cp\u003e18.7.3 Conditional independence explanation 366\u003c\/p\u003e \u003cp\u003e18.7.4 Marginalization explanation 366\u003c\/p\u003e \u003cp\u003e18.7.5 Jacobian explanation 367\u003c\/p\u003e \u003cp\u003e18.7.6 Equivalence of the independence assumptions 367\u003c\/p\u003e \u003cp\u003e18.7.7 Probability kinematics explanation 368\u003c\/p\u003e \u003cp\u003e18.7.8 Bayesian explanation 369\u003c\/p\u003e \u003cp\u003e18.8 Kullback–Leibler optimality 370\u003c\/p\u003e \u003cp\u003e18.9 Link with statistical potentials 371\u003c\/p\u003e \u003cp\u003e18.10 Conclusions and outlook 372\u003c\/p\u003e \u003cp\u003eAcknowledgments 373\u003c\/p\u003e \u003cp\u003eReferences 373\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 MAD-Bayes matching and alignment for labelled and unlabelled configurations 377\u003cbr\u003e \u003c\/b\u003e\u003ci\u003ePeter J. Green\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 377\u003c\/p\u003e \u003cp\u003e19.2 Modelling protein matching and alignment 378\u003c\/p\u003e \u003cp\u003e19.3 Gap priors and related models 379\u003c\/p\u003e \u003cp\u003e19.4 MAD-Bayes 381\u003c\/p\u003e \u003cp\u003e19.5 MAD-Bayes for unlabelled matching and alignment 382\u003c\/p\u003e \u003cp\u003e19.6 Omniparametric optimisation of the objective function 384\u003c\/p\u003e \u003cp\u003e19.7 MAD-Bayes in the sequence-labelled case 384\u003c\/p\u003e \u003cp\u003e19.8 Other kinds of labelling 385\u003c\/p\u003e \u003cp\u003e19.9 Simultaneous alignment of multiple configurations 385\u003c\/p\u003e \u003cp\u003e19.10 Beyond MAD-Bayes to posterior approximation? 386\u003c\/p\u003e \u003cp\u003e19.11 Practical uses of MAD-Bayes approximations 387\u003c\/p\u003e \u003cp\u003eAcknowledgments 388\u003c\/p\u003e \u003cp\u003eReferences 388\u003c\/p\u003e \u003cp\u003eIndex 391\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIan L. Dryden\u003c\/b\u003e, University of Nottingham, UK\u003c\/p\u003e \u003cp\u003e\u003cb\u003eJohn T. Kent\u003c\/b\u003e, University of Leeds, UK\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA 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\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eGeometry Driven Statistics\u003c\/i\u003e 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.\u003c\/p\u003e Summarizing the state of the art, examining some new developments and presenting a vision for the future, \u003ci\u003eGeometry Driven Statistics\u003c\/i\u003e 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.","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989283586277,"sku":"NP9781118866573","price":134.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118866573.jpg?v=1761783513","url":"https:\/\/k12savings.com\/es\/products\/geometry-driven-statistics-isbn-9781118866573","provider":"K12savings","version":"1.0","type":"link"}