Differential Geometry and Statistics

ISBN-13: 9780412398605 / Angielski / Twarda / 1993 / 288 str.

M. K. Murray;Rice J W; Murray Murray

Opis

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.

Recenzje

"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

Spis treści

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.

O autorze

M.K. Murray