Differential Geometry and Statistics

by M.K. Murray, J.W. Rice

Overview

This book explains why geometry should enter into parametric statistics and how the theory of asymptotic expansions involves a form of higher-order differential geometry. It gives some new explanations of geometric ideas from a first principles point of view as far as geometry is concerned.

Product Details

ISBN-13:	9780412398605
Publisher:	Taylor & Francis
Publication date:	04/01/1993
Series:	Chapman & Hall/CRC Monographs on Statistics and Applied Probability , #48
Edition description:	New Edition
Pages:	288
Product dimensions:	6.00(w) x 9.00(h) x (d)
Age Range:	18 Years

About the Author

M.K. Murray

Table of Contents

1. The geometry of exponential families 2. Calculus on manifolds 3. Statistical Manifolds 4. Connections 5. Curvature 6. Information metrics and statistical divergences 7. Asymptotics 8. Bundles and tensors 9. Higher-order geometry

Editorial Reviews

"This book does an excellent job of explaining... geometrical ideas from a statistical point of view, using statistical examples as opposed to, for example, dynamical examples to illustrate the geometric concepts. It should prove most helpful in enlarging the typical statistician's working geometric vocabulary."
-Short Book Reviews of the ISI
"It is particularly good on the... problem of when to use coordinates and indices, and when to use the more geometric coordinate-free methods. Examples of this are its treatments of the affine connection and of the string theory of Barndorff-Nielsen, both of which are excellent. The first of these concepts is probably the most sophisticated that has been used in statistical applications. It can be viewed in many different ways, not all of which are necessarily useful to the statistician; the approach taken in the book is both relevant and clear."
-Bulletin of London Mathematical Society

From the Publisher

An introduction to the modern coordinate-free approach to differential geometry in such a way that statisticians can understand it and apply it to statistics. Beginning with the simplest differentiable manifolds, walks through such territory as the general theory, the Fisher information metric, and asymptotics, to arrive at the cutting-edge topic of vector bundles and jets and their applications to the theory of strings. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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