Geometry Driven Statistics

Author : Ian L. Dryden,John T. Kent
Publisher : John Wiley & Sons
Page : 436 pages
File Size : 49,5 Mb
Release : 2015-09-28
Category : Mathematics
ISBN : 9781118866573

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Geometry Driven Statistics by Ian L. Dryden,John T. Kent Pdf

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.

Author : Ian L. Dryden,John T. Kent
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 47,9 Mb
Release : 2015-09-03
Category : Mathematics
ISBN : 9781118866603

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Geometry Driven Statistics by Ian L. Dryden,John T. Kent Pdf

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.

Author : Ovidiu Calin,Constantin Udrişte
Publisher : Springer
Page : 375 pages
File Size : 50,5 Mb
Release : 2014-07-17
Category : Mathematics
ISBN : 9783319077796

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Geometric Modeling in Probability and Statistics by Ovidiu Calin,Constantin Udrişte Pdf

This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Author : M.K. Murray
Publisher : Routledge
Page : 293 pages
File Size : 49,9 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351455121

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Differential Geometry and Statistics by M.K. Murray Pdf

Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff- Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.

Author : Wilfrid S. Kendall
Publisher : Unknown
Page : 128 pages
File Size : 43,8 Mb
Release : 2017
Category : Electronic books
ISBN : 0203738276

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Stochastic Geometry by Wilfrid S. Kendall Pdf

"Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themeso considerations of geometric sampling bias issueso tesselationso shapeo random setso image analysiso spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo"--Provided by publisher.

Author : J. S. Marron,Ian L. Dryden
Publisher : CRC Press
Page : 436 pages
File Size : 45,8 Mb
Release : 2021-11-18
Category : Computers
ISBN : 9781351189668

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Object Oriented Data Analysis by J. S. Marron,Ian L. Dryden Pdf

Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.

Author : Ovidiu Calin,Constantin Udriste
Publisher : Springer
Page : 375 pages
File Size : 50,5 Mb
Release : 2014-08-01
Category : Mathematics
ISBN : 3319077783

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Geometric Modeling in Probability and Statistics by Ovidiu Calin,Constantin Udriste Pdf

This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Author : Regina Y. Liu,Robert Joseph Serfling,Diane L. Souvaine
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 45,8 Mb
Release : 2006
Category : Geometry
ISBN : 9780821835968

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Data Depth by Regina Y. Liu,Robert Joseph Serfling,Diane L. Souvaine Pdf

The book is a collection of some of the research presented at the workshop of the same name held in May 2003 at Rutgers University. The workshop brought together researchers from two different communities: statisticians and specialists in computational geometry. The main idea unifying these two research areas turned out to be the notion of data depth, which is an important notion both in statistics and in the study of efficiency of algorithms used in computational geometry. Many of the articles in the book lay down the foundations for further collaboration and interdisciplinary research. Information for our distributors: Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).

Author : David J. Saville,Graham R. Wood
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207474

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Statistical Methods by David J. Saville,Graham R. Wood Pdf

The aim of this book is to present the mathematics underlying elementary statistical methods in as simple a manner as possible. These methods include independent and paired sample t-tests, analysis of variance, regression, and the analysis of covariance. The author's principle tool is the use of geometric ideas to provide more visual insight and to make the theory accessible to a wider audience than is usually possible.

Author : Frank Nielsen
Publisher : Springer Nature
Page : 274 pages
File Size : 41,6 Mb
Release : 2021-03-14
Category : Science
ISBN : 9783030654597

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Progress in Information Geometry by Frank Nielsen Pdf

This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI’2019 – Geometric Science of Information that was held at ENAC, Toulouse (France).

Author : John T. Kent,Kanti V. Mardia
Publisher : John Wiley & Sons
Page : 404 pages
File Size : 42,9 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9780471632054

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Spatial Analysis by John T. Kent,Kanti V. Mardia Pdf

SPATIAL ANALYSIS Explore the foundations and latest developments in spatial statistical analysis In Spatial Analysis, two distinguished authors deliver a practical and insightful exploration of the statistical investigation of the interdependence of random variables as a function of their spatial proximity. The book expertly blends theory and application, offering numerous worked examples and exercises at the end of each chapter. Increasingly relevant to fields as diverse as epidemiology, geography, geology, image analysis, and machine learning, spatial statistics is becoming more important to a wide range of specialists and professionals. The book includes: Thorough introduction to stationary random fields, intrinsic and generalized random fields, and stochastic models Comprehensive exploration of the estimation of spatial structure Practical discussion of kriging and the spatial linear model Spatial Analysis is an invaluable resource for advanced undergraduate and postgraduate students in statistics, data science, digital imaging, geostatistics, and agriculture. It’s also an accessible reference for professionals who are required to use spatial models in their work.

Author : Anuj Srivastava,Eric P. Klassen
Publisher : Springer
Page : 447 pages
File Size : 53,9 Mb
Release : 2016-10-03
Category : Mathematics
ISBN : 9781493940202

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Functional and Shape Data Analysis by Anuj Srivastava,Eric P. Klassen Pdf

This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Author : Shun'ichi Amari
Publisher : IMS
Page : 254 pages
File Size : 52,9 Mb
Release : 1987
Category : Geometry, Differential
ISBN : 0940600129

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Differential Geometry in Statistical Inference by Shun'ichi Amari Pdf

Author : Brigitte Le Roux,Henry Rouanet
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 51,8 Mb
Release : 2004-06-29
Category : Mathematics
ISBN : 1402022352

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Geometric Data Analysis by Brigitte Le Roux,Henry Rouanet Pdf

Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benzécri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including Bayesian methods. Chapter 9, Research Case Studies, is nearly a book in itself; it presents the methodology in action on three extensive applications, one for medicine, one from political science, and one from education (data borrowed from the Stanford computer-based Educational Program for Gifted Youth ). Thus the readership of the book concerns both mathematicians interested in the applications of mathematics, and researchers willing to master an exceptionally powerful approach of statistical data analysis.

Author : M. K. Murray,John Rice
Publisher : Springer
Page : 272 pages
File Size : 53,6 Mb
Release : 2013-10-29
Category : Mathematics
ISBN : 1489933077

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Differential Geometry and Statistics by M. K. Murray,John Rice Pdf

Several years ago our statistical friends and relations introduced us to the work of Amari and Barndorff-Nielsen on applications of differential geometry to statistics. This book has arisen because we believe that there is a deep relationship between statistics and differential geometry and moreoever that this relationship uses parts of differential geometry, particularly its 'higher-order' aspects not readily accessible to a statistical audience from the existing literature. It is, in part, a long reply to the frequent requests we have had for references on differential geometry! While we have not gone beyond the path-breaking work of Amari and Barndorff Nielsen in the realm of applications, our book gives some new explanations of their ideas from a first principles point of view as far as geometry is concerned. In particular it seeks to explain why geometry should enter into parametric statistics, and how the theory of asymptotic expansions involves a form of higher-order differential geometry. The first chapter of the book explores exponential families as flat geometries. Indeed the whole notion of using log-likelihoods amounts to exploiting a particular form of flat space known as an affine geometry, in which straight lines and planes make sense, but lengths and angles are absent. We use these geometric ideas to introduce the notion of the second fundamental form of a family whose vanishing characterises precisely the exponential families.