Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Geometric modeling in probability and statistics / Ovidiu Calin and Constantin Udriste.

By: Contributor(s): Material type: TextTextPublication details: Switzerland : Springer, 2014.Description: xxiii, 375 p. ; illustrationsISBN:
  • 9783319077789
Subject(s): DDC classification:
  • 000SA.01 23 C154
Contents:
I. The Geometry of Statistical Models -- 1. Statistical Models -- 2. Explicit Examples -- 3. Entropy on Statistical Models -- 4. Kullback-Leibler Relative Entropy -- 5. Informational Energy -- 6. Maximum Entropy Distributions -- II. Statistical Manifolds -- 7. An Introduction to Manifolds -- 8. Dualistic Structure -- 9. Dual Volume Elements -- 10. Dual Laplacians -- 11. Contrast Functions Geometry -- 12. Contrast Functions on Statistical Models -- 13. Statistical Submanifolds -- Appendix A: Information Geometry Calculator-- Bibliography-- Index.
Summary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.

Includes bibliographical references and index.

I. The Geometry of Statistical Models --
1. Statistical Models --
2. Explicit Examples --
3. Entropy on Statistical Models --
4. Kullback-Leibler Relative Entropy --
5. Informational Energy --
6. Maximum Entropy Distributions --

II. Statistical Manifolds --
7. An Introduction to Manifolds --
8. Dualistic Structure --
9. Dual Volume Elements --
10. Dual Laplacians --
11. Contrast Functions Geometry --
12. Contrast Functions on Statistical Models --
13. Statistical Submanifolds --
Appendix A: Information Geometry Calculator--
Bibliography--
Index.

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.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in