Information Theory and Statistics: A Tutorial

Author(s): Imre Csiszár;Paul C. Shields

Source:
    Journal:Foundations and Trends® in Communications and Information Theory
    ISSN Print:1567-2190,  ISSN Online:1567-2328
    Publisher:Now Publishers
    Volume 1 Number 4,

Document Type: Article
Pages: 112(417-528)
DOI: 10.1516/0100000004

Abstract: This tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The information measure known as information divergence or Kullback-Leibler distance or relative entropy plays a key role, often with a geometric flavor as an analogue of squared Euclidean distance, as in the concepts of I-projection, I-radius and I-centroid. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an “information geometry” background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory.

Full Text