Differential-Geometrical Methods in Statistics
Title | Differential-Geometrical Methods in Statistics PDF eBook |
Author | Shun-ichi Amari |
Publisher | Springer Science & Business Media |
Total Pages | 302 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461250560 |
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 Theory of Statistics
Title | Differential Geometrical Theory of Statistics PDF eBook |
Author | Frédéric Barbaresco |
Publisher | MDPI |
Total Pages | 473 |
Release | 2018-04-06 |
Genre | Electronic book |
ISBN | 3038424242 |
This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy
Differential Geometry and Statistics
Title | Differential Geometry and Statistics PDF eBook |
Author | M.K. Murray |
Publisher | Routledge |
Total Pages | 164 |
Release | 2017-10-19 |
Genre | Mathematics |
ISBN | 1351455117 |
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.
Differential Geometry in Statistical Inference
Title | Differential Geometry in Statistical Inference PDF eBook |
Author | Shun'ichi Amari |
Publisher | IMS |
Total Pages | 254 |
Release | 1987 |
Genre | Geometry, Differential |
ISBN | 9780940600126 |
Differential Geometrical Theory of Statistics
Title | Differential Geometrical Theory of Statistics PDF eBook |
Author | |
Publisher | |
Total Pages | |
Release | 2017 |
Genre | Electronic book |
ISBN | 9783038424253 |
Differential Geometry and Statistics
Title | Differential Geometry and Statistics PDF eBook |
Author | M.K. Murray |
Publisher | Routledge |
Total Pages | 293 |
Release | 2017-10-19 |
Genre | Mathematics |
ISBN | 1351455125 |
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.
Differential Geometrical Foundations of Information Geometry: Geometry of Statistical Manifolds and Divergences
Title | Differential Geometrical Foundations of Information Geometry: Geometry of Statistical Manifolds and Divergences PDF eBook |
Author | Hiroshi Matsuzoe |
Publisher | |
Total Pages | 350 |
Release | 2015-11-30 |
Genre | Mathematics |
ISBN | 9789814618762 |