Information Geometry Near Randomness and Near Independence
This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate proc
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1953
Khadiga A. Arwini · Christopher T.J. Dodson
Information Geometry Near Randomness and Near Independence
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Authors Khadiga A. Arwini
Christopher T.J. Dodson
Al-Fateh University Faculty of Sciences Mathematics Department Box 13496 Tripoli, Libya [email protected]
University of Manchester School of Mathematics Manchester M13 9PL, United Kingdom [email protected]
ISBN: 978-3-540-69391-8 e-ISBN: 978-3-540-69393-2 DOI: 10.1007/978-3-540-69393-2 Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2008930087 Mathematics Subject Classification (2000): 53B50, 60D05, 62B10, 62P35, 74E35, 92D20 c 2008 Springer-Verlag Berlin Heidelberg ° This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: SPi Publishing Services Printed on acid-free paper 987654321 springer.com
Preface
The main motivation for this book lies in the breadth of applications in which a statistical model is used to represent small departures from, for example, a Poisson process. Our approach uses information geometry to provide a common context but we need only rather elementary material from differential geometry, information theory and mathematical statistics. Introductory sections serve together to help those interested from the applications side in making use of our methods and results. We have available Mathematica notebooks to perform many of the computations for those who wish to pursue their own calculations or developments. Some 44 years ago, the second author first encountered, at about the same time, differential geometry via relativity from Weyl’s book [209] during undergraduate studies and information theory from Tribus [200, 201] via spatial statistical processes while working on research projects at Wiggins Teape Research and Development Ltd—cf. the Foreword in [196] and [170, 47, 58]. Having started work there as a student laboratory assistant in 1959, this research environment engendered a recognition of the importance of international collaboration, and a lifelong research interest in randomness and near-Poisson statistical geometric processes, persisting at various rates through a career mainly involved with global differential geometry. From corr
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