Informative Geometry of Probability Spaces

Abstract

This paper is concerned with the geometrical properties that are induced by the local information contents and structures of the parameter space of probability distributions. Of particular interest in this investigation is the Rao distance which is the geodesic distance induced by the differential metric associated with the Fisher information matrix of the parameter space. Moreover, following Efron, Dawid and Amari, some affine connections are introduced into the informative geometry of parameter space and thereby elucidating the role of the curvature in statistical studies. In addition, closed form expressions of the Rao distances for certain families of probability distributions are given and discussed.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1984
Accession Number
ADA150510

Entities

People

  • J. Burbea

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Classification
  • Complex Variables
  • Curvature
  • Differential Geometry
  • Geometric Forms
  • Geometry
  • Lines (Geometry)
  • Multivariate Analysis
  • New York
  • Normal Distribution
  • Probability
  • Probability Distributions
  • Random Variables
  • Security
  • Statistical Inference

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Statistical inference.

Technology Areas

  • Space
  • Space - Space Objects