Differential Geometrical Methods In Statistics
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Differential Geometrical Methods in Statistics
Author | : Shun-ichi Amari |
Publsiher | : Springer Science & Business Media |
Total Pages | : 302 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461250562 |
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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
Differential Geometrical Methods in Statistics
Author | : Shun-ichi Amari |
Publsiher | : Springer |
Total Pages | : 294 |
Release | : 1990-02-14 |
Genre | : Mathematics |
ISBN | : 0387960562 |
Download Differential Geometrical Methods in Statistics Book in PDF, Epub and Kindle
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
Differential Geometry in Statistical Inference
Author | : Shun'ichi Amari |
Publsiher | : IMS |
Total Pages | : 254 |
Release | : 1987 |
Genre | : Geometry, Differential |
ISBN | : 0940600129 |
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Differential Geometrical Theory of Statistics
Author | : Frédéric Barbaresco,Frank Nielsen |
Publsiher | : MDPI |
Total Pages | : 473 |
Release | : 2018-04-06 |
Genre | : Electronic book |
ISBN | : 9783038424246 |
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This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy
Differential Geometry and Statistics
Author | : M.K. Murray |
Publsiher | : Routledge |
Total Pages | : 164 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 9781351455114 |
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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.
Applications of Differential Geometry to Econometrics
Author | : Paul Marriott,Mark Salmon |
Publsiher | : Cambridge University Press |
Total Pages | : 342 |
Release | : 2000-08-31 |
Genre | : Business & Economics |
ISBN | : 0521651166 |
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Originally published in 2000, this volume was an early example of the application of differential geometry to econometrics.
Differential Geometry and Statistics
Author | : M.K. Murray |
Publsiher | : Routledge |
Total Pages | : 293 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 9781351455121 |
Download Differential Geometry and Statistics Book in PDF, Epub and Kindle
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.
Methods of Information Geometry
Author | : Shun-ichi Amari,Hiroshi Nagaoka |
Publsiher | : American Mathematical Soc. |
Total Pages | : 220 |
Release | : 2000 |
Genre | : Computers |
ISBN | : 0821843028 |
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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.