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Book review

Author(s) Murray, M.K.
Rice, J.W.
Title Differential Geometry and Statistics
Publisher Chapman & Hall
Year of publication 1993
Reviewed by Balan Vladimir

The aim of the book is to introduce the modern coordinate-free approach to differential geometry in a manner accessible to statisticians.

The extensive research experience of the authors in differential geometry and its applications to statistics is reflected in the various topics covered by the volume: the relevance of affine spaces to exponential families, differentiable manifolds, the Fisher information metric, the Amari connections and asymptotics, vector and principal bundles, jets, and their applications to the theory of strings.

A brief but well-selected set of references, a notation index and a subject index are also included.

The book is requiring from the reader graduate-level knowledge, and is written in a pleasant discursive style. It contains useful remarks and examples, and exercises at the end of each chapter.

It is recommended to researchers at the cutting edge of statistics and differential geometry, and represents a beneficial investment for libraries and individuals.