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Differential Geometry and Statistics (Monographs on Statistics and Applied Probability, Band 48) - Hardcover

Buch 72 von 110: ISSN

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

 
9780412398605: Differential Geometry and Statistics (Monographs on Statistics and Applied Probability, Band 48)
Hardcover
ISBN 10: 0412398605 ISBN 13: 9780412398605
Verlag: Chapman and Hall/CRC, 1993

Inhaltsangabe

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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Über die Autorin bzw. den Autor

M.K. Murray

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Verlag
Chapman and Hall/CRC
Erscheinungsdatum
1993
Sprache
Englisch
ISBN 10 
0412398605
ISBN 13 
9780412398605
Einband
Gebundene Ausgabe
Anzahl der Seiten
292
Herausgeber
Cox D.R., Reid N., Isham Valerie, Tibshirani R.J., Louis Thomas A., Tong Howell, Keiding Niels
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Taylor & Francis Verlag GmbH
GPSR@taylorandfrancis.com

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