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Differential Geometry and Statistics

M.K. Murray J.W. Rice



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Chapman & Hall/CRC
01 April 1993
Differential & Riemannian geometry; Analytic geometry; Probability & statistics
Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians is the lack of a suitable text introducing the modern co-ordinate free approach to differential geometry in a manner accessible to statisticians. This book aims to fill this gap. The authors bring to the book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differential manifolds - affine spaces and their relevance to exponential families and passes into the general theory, the Fisher information metric, the Amari connection and asymptotics. It culminates in the theory of the vector bundles, principle bundles and jets and their application to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry.
By:   M.K. Murray, J.W. Rice
Imprint:   Chapman & Hall/CRC
Country of Publication:   United States
Volume:   48
Dimensions:   Height: 229mm,  Width: 152mm,  Spine: 20mm
Weight:   544g
ISBN:   9780412398605
ISBN 10:   0412398605
Series:   Chapman & Hall/CRC Monographs on Statistics and Applied Probability
Pages:   288
Publication Date:   01 April 1993
Audience:   College/higher education ,  Professional and scholarly ,  Primary ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
The Geometry of Exponential Families. Calculus on Manifolds. Statistical Manifolds. Connections. Curvature. Information Metrices and Statistical Divergences. Asymptotics. Bundles and Tensors. Higher Order Geometry. References. Index.

Reviews for Differential Geometry and Statistics

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

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