Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Differential Geometrical Theory Of Statistics
Download Differential Geometrical Theory Of Statistics full books in PDF, epub, and Kindle. Read online Differential Geometrical Theory Of Statistics ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Differential-Geometrical Methods in Statistics by : Shun-ichi Amari
Download or read book Differential-Geometrical Methods in Statistics written by Shun-ichi Amari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2
Book Synopsis Differential Geometrical Theory of Statistics by : Frédéric Barbaresco
Download or read book Differential Geometrical Theory of Statistics written by Frédéric Barbaresco and published by MDPI. This book was released on 2018-04-06 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy
Book Synopsis Differential Geometry and Statistics by : M.K. Murray
Download or read book Differential Geometry and Statistics written by M.K. Murray and published by Routledge. This book was released on 2017-10-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential Geometry in Statistical Inference by : Shun'ichi Amari
Download or read book Differential Geometry in Statistical Inference written by Shun'ichi Amari and published by IMS. This book was released on 1987 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometrical Theory of Statistics by :
Download or read book Differential Geometrical Theory of Statistics written by and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry and Statistics by : M.K. Murray
Download or read book Differential Geometry and Statistics written by M.K. Murray and published by Routledge. This book was released on 2017-10-19 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Information Geometry and Its Applications by : Shun-ichi Amari
Download or read book Information Geometry and Its Applications written by Shun-ichi Amari and published by Springer. This book was released on 2016-02-02 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Book Synopsis Methods of Information Geometry by : Shun-ichi Amari
Download or read book Methods of Information Geometry written by Shun-ichi Amari and published by American Mathematical Soc.. This book was released on 2000 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis.
Book Synopsis Differential Geometrical Foundations of Information Geometry: Geometry of Statistical Manifolds and Divergences by : Hiroshi Matsuzoe
Download or read book Differential Geometrical Foundations of Information Geometry: Geometry of Statistical Manifolds and Divergences written by Hiroshi Matsuzoe and published by . This book was released on 2015-11-30 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Modeling in Probability and Statistics by : Ovidiu Calin
Download or read book Geometric Modeling in Probability and Statistics written by Ovidiu Calin and published by Springer. This book was released on 2014-07-17 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometrical Methods of Mathematical Physics by : Bernard F. Schutz
Download or read book Geometrical Methods of Mathematical Physics written by Bernard F. Schutz and published by Cambridge University Press. This book was released on 1980-01-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Book Synopsis Geometric Aspects of Probability Theory and Mathematical Statistics by : V.V. Buldygin
Download or read book Geometric Aspects of Probability Theory and Mathematical Statistics written by V.V. Buldygin and published by Springer Science & Business Media. This book was released on 2000-08-31 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the usefulness of geometric methods in probability theory and mathematical statistics, and shows close relationships between these disciplines and convex analysis. Deep facts and statements from the theory of convex sets are discussed with their applications to various questions arising in probability theory, mathematical statistics, and the theory of stochastic processes. The book is essentially self-contained, and the presentation of material is thorough in detail. Audience: The topics considered in the book are accessible to a wide audience of mathematicians, and graduate and postgraduate students, whose interests lie in probability theory and convex geometry.
Book Synopsis Differential Geometry and Analysis on CR Manifolds by : Sorin Dragomir
Download or read book Differential Geometry and Analysis on CR Manifolds written by Sorin Dragomir and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study
Book Synopsis Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis by : Victor Patrangenaru
Download or read book Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis written by Victor Patrangenaru and published by CRC Press. This book was released on 2015-09-18 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: A New Way of Analyzing Object Data from a Nonparametric ViewpointNonparametric Statistics on Manifolds and Their Applications to Object Data Analysis provides one of the first thorough treatments of the theory and methodology for analyzing data on manifolds. It also presents in-depth applications to practical problems arising in a variety of fields
Book Synopsis Applications of Differential Geometry to Econometrics by : Paul Marriott
Download or read book Applications of Differential Geometry to Econometrics written by Paul Marriott and published by Cambridge University Press. This book was released on 2000-08-31 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 2000, this volume was an early example of the application of differential geometry to econometrics.
Book Synopsis Introduction to Differential Geometry by : Joel W. Robbin
Download or read book Introduction to Differential Geometry written by Joel W. Robbin and published by Springer Nature. This book was released on 2022-01-12 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Book Synopsis Differential Geometric Methods in Theoretical Physics by : Ling-Lie Chau
Download or read book Differential Geometric Methods in Theoretical Physics written by Ling-Lie Chau and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 795 pages. Available in PDF, EPUB and Kindle. Book excerpt: After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit ful again. Many of the leading specialists of both fields became involved in this devel opment. This process even led to the discovery of previously unsuspected connections between various subfields of physics and mathematics. In mathematics this concerns in particular knots von Neumann algebras, Kac-Moody algebras, integrable non-linear partial differential equations, and differential geometry in low dimensions, most im portantly in three and four dimensional spaces. In physics it concerns gravity, string theory, integrable classical and quantum field theories, solitons and the statistical me chanics of surfaces. New discoveries in these fields are made at a rapid pace. This conference brought together active researchers in these areas, reporting their results and discussing with other participants to further develop thoughts in future new directions. The conference was attended by SO participants from 15 nations. These proceedings document the program and the talks at the conference. This conference was preceded by a two-week summer school. Ten lecturers gave extended lectures on related topics. The proceedings of the school will also be published in the NATO-AS[ volume by Plenum. The Editors vii ACKNOWLEDGMENTS We would like to thank the many people who have made the conference a success. Furthermore, ·we appreciate the excellent talks. The active participation of everyone present made the conference lively and stimulating. All of this made our efforts worth while.
