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Author: Shun'ichi Amari
Publisher: IMS
Published: 1987
Total Pages: 254
ISBN-13: 9780940600126
DOWNLOAD EBOOKDownload 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:
Author: Shunʼichi Amari
Publisher:
Published: 2008*
Total Pages: 240
ISBN-13:
DOWNLOAD EBOOKThis e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.
Download or read book Differential Geometry in Statistical Inference written by Shunʼichi Amari and published by . This book was released on 2008* with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.
Author: M.K. Murray
Publisher: Routledge
Published: 2017-10-19
Total Pages: 164
ISBN-13: 1351455117
DOWNLOAD EBOOKSeveral 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.
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 164 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.
Author: Shun-ichi Amari
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 302
ISBN-13: 1461250560
DOWNLOAD EBOOKFrom 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
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
Author: Shun-ichi Amari
Publisher: American Mathematical Soc.
Published: 2000
Total Pages: 220
ISBN-13: 9780821843024
DOWNLOAD EBOOKInformation 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.
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.
Author: Shun-ichi Amari
Publisher: Springer
Published: 2016-02-02
Total Pages: 378
ISBN-13: 4431559787
DOWNLOAD EBOOKThis 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.
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.
Author: Hiroshi Matsuzoe
Publisher:
Published: 2015-11-30
Total Pages: 350
ISBN-13: 9789814618762
DOWNLOAD EBOOKDownload 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:
Author: Masanobu Taniguchi
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 671
ISBN-13: 146121162X
DOWNLOAD EBOOKThe primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.
Download or read book Asymptotic Theory of Statistical Inference for Time Series written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.
Author: Paul Marriott
Publisher: Cambridge University Press
Published: 2000-08-31
Total Pages: 342
ISBN-13: 9780521651165
DOWNLOAD EBOOKOriginally published in 2000, this volume was an early example of the application of differential geometry to econometrics.
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.
Author: Robert E. Kass
Publisher: Wiley-Interscience
Published: 1997-07-17
Total Pages: 384
ISBN-13:
DOWNLOAD EBOOKDifferential geometry provides an aesthetically appealing and often revealing view of statistical inference. Beginning with an elementary treatment of one-parameter statistical models and ending with an overview of recent developments, this is the first book to provide an introduction to the subject that is largely accessible to readers not already familiar with differential geometry. It also gives a streamlined entry into the field to readers with richer mathematical backgrounds. Much space is devoted to curved exponential families, which are of interest not only because they may be studied geometrically but also because they are analytically convenient, so that results may be derived rigorously. In addition, several appendices provide useful mathematical material on basic concepts in differential geometry. Topics covered include the following: Basic properties of curved exponential families Elements of second-order, asymptotic theory The Fisher-Efron-Amari theory of information loss and recovery Jeffreys-Rao information-metric Riemannian geometry Curvature measures of nonlinearity Geometrically motivated diagnostics for exponential family regression Geometrical theory of divergence functions A classification of and introduction to additional work in the field
Download or read book Geometrical Foundations of Asymptotic Inference written by Robert E. Kass and published by Wiley-Interscience. This book was released on 1997-07-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry provides an aesthetically appealing and often revealing view of statistical inference. Beginning with an elementary treatment of one-parameter statistical models and ending with an overview of recent developments, this is the first book to provide an introduction to the subject that is largely accessible to readers not already familiar with differential geometry. It also gives a streamlined entry into the field to readers with richer mathematical backgrounds. Much space is devoted to curved exponential families, which are of interest not only because they may be studied geometrically but also because they are analytically convenient, so that results may be derived rigorously. In addition, several appendices provide useful mathematical material on basic concepts in differential geometry. Topics covered include the following: Basic properties of curved exponential families Elements of second-order, asymptotic theory The Fisher-Efron-Amari theory of information loss and recovery Jeffreys-Rao information-metric Riemannian geometry Curvature measures of nonlinearity Geometrically motivated diagnostics for exponential family regression Geometrical theory of divergence functions A classification of and introduction to additional work in the field
