Geometric Modeling in Probability and Statistics

  • Ovidiu Calin
  • Constantin Udrişte

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. The Geometry of Statistical Models

    1. Front Matter
      Pages 1-1
    2. Ovidiu Calin, Constantin Udrişte
      Pages 3-49
    3. Ovidiu Calin, Constantin Udrişte
      Pages 51-75
    4. Ovidiu Calin, Constantin Udrişte
      Pages 77-110
    5. Ovidiu Calin, Constantin Udrişte
      Pages 111-131
    6. Ovidiu Calin, Constantin Udrişte
      Pages 133-163
    7. Ovidiu Calin, Constantin Udrişte
      Pages 165-187
  3. Statistical Manifolds

    1. Front Matter
      Pages 189-189
    2. Ovidiu Calin, Constantin Udrişte
      Pages 191-222
    3. Ovidiu Calin, Constantin Udrişte
      Pages 223-255
    4. Ovidiu Calin, Constantin Udrişte
      Pages 257-290
    5. Ovidiu Calin, Constantin Udrişte
      Pages 291-302
    6. Ovidiu Calin, Constantin Udrişte
      Pages 303-320
    7. Ovidiu Calin, Constantin Udrişte
      Pages 321-334
    8. Ovidiu Calin, Constantin Udrişte
      Pages 335-355
  4. Back Matter
    Pages 357-375

About this book

Introduction

This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields.

This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Keywords

Entropy Fisher information Informational geometry Probability density function Statistical manifolds

Authors and affiliations

  • Ovidiu Calin
    • 1
  • Constantin Udrişte
    • 2
  1. 1.Department of MathematicsEastern Michigan UniversityYpsilantiUSA
  2. 2.Faculty of Applied Sciences, Department of Mathematics-InformaticsUniversity Politehnica of BucharestBucharestRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-07779-6
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-07778-9
  • Online ISBN 978-3-319-07779-6
  • About this book
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