Differential Geometry and Statistics

Name: Differential Geometry and Statistics
Brand: Taylor & Francis Ltd
SKU: 9780412398605
Price: 1091.12 PLN
Availability: InStock

Autor: M. K. Murray, John Rice

Język:

Oprawa: Twarda

Wydawca: Taylor & Francis Ltd

Dostępność: 50 % szansa

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Several years ago our statistical friends and relations introduced us to the work of Amari and Barnd...

Informacje o książce

Autor

M. K. Murray, John Rice

Język

Angielski

Oprawa

Książka - Twarda

Data wydania

1993

strony

288

EAN

9780412398605

ISBN

0412398605

Enbook ID

02636092

Wydawca

Taylor & Francis Ltd

Waga

560

Wymiary

152 x 229 x 25

Pełny opis

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.

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