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Exploratory Data Analysis Using Fisher Information

  • B. Roy Frieden
  • Robert A. Gatenby

Table of contents

  1. Front Matter
    Pages i-xiii
  2. B. Roy Frieden, Raymond J. Hawkins, Joseph L. D’Anna
    Pages 42-73
  3. Robert A. Gatenby, B. Roy Frieden
    Pages 74-118
  4. Angelo Plastino, Angelo Ricardo Plastino
    Pages 119-154
  5. B.Roy Frieden, Bernard H. Soffer
    Pages 155-180
  6. Ravi. C. Venkatesan
    Pages 181-216
  7. Audrey L. Mayer, Christopher Pawlowski, Brian D. Fath, Heriberto Cabezas
    Pages 217-244
  8. B. Roy Frieden, Robert A. Gatenby
    Pages 245-284
  9. M. I. Yolles, B. Roy Frieden
    Pages 285-335
  10. Back Matter
    Pages 337-363

About this book

Introduction

The basic goal of a research scientist is to understand a given, unknown system. This innovative book develops a systematic approach for achieving this goal. All science is ultimately dependent upon observation which, in turn, requires a flow of information. Fisher information, in particular, is found to provide the key to understanding the system. It is developed as a new tool of exploratory data analysis, and is applied to a wide scope of systems problems. These range from molecules in a gas to biological organisms in their ecologies, to the socio-economic organization of people in their societies, to the physical constants in the universe and, ultimately, to proto-universes in the multiverse.

Examples of system input-output laws discovered by the approach include the famous quarter-power laws of biology and the Tobin q-theory of optimized economic investment. System likelihood laws that can be determined include the probability density functions defining in situ cancer growth and a wide class of systems (thermodynamic, economic, cryptographic) obeying Schrodinger-like equations. Novel uncertainty principles in the fields of biology and economics are also found to hold.

B. Roy Frieden and Robert A. Gatenby are professors at the University of Arizona. Frieden is in the College of Optics, and Gatenby is Chairman of the Radiology Dept. at the Arizona Health Sciences Center. Frieden has pioneered the use of information for developing image restoration approaches, and for understanding the physics of unknown systems, both nonliving and living. Gatenby has actively promoted the study of information as a determinant of healthy and malignant growth processes, and has developed integrated mathematical models and empirical techniques for this purpose.

Keywords

EPI Entropy Estimation of Probability Laws Estimation of System Laws Fisher Information Fluctuations in Financial Issues Information Pattern Recognition Physical Information Power Laws Sociocultural Organization data analysis information theory organization uncertainty

Editors and affiliations

  • B. Roy Frieden
    • 1
  • Robert A. Gatenby
    • 2
  1. 1.College of Optical SciencesUniversity of ArizonaTucsonUSA
  2. 2.Radiology DepartmentArizona Health Sciences CenterTucsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84628-777-0
  • Copyright Information Springer-Verlag London 2007
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-1-84628-506-6
  • Online ISBN 978-1-84628-777-0
  • Buy this book on publisher's site