APPLICATION OF WALSH TRANSFORM TO STATISTICAL ANALYSIS,

Abstract

Harmonic analysis of probability distribution functions has long served an important function in the treatment of stochastic systems. The tasks of generating moments and distributions of sums have effectively been executed in the Fourier spectrum. This paper explores the properties of the Walsh-Hadamard transform of probability functions of discrete random variables. Many analogies can be drawn between Fourier and Walsh analysis; in particular, it is shown that moments can be generated taking the Gibb's derivative of the Walsh spectrum, and products of Walsh spectra yield the distribution of dyadic sums. Stochastic systems with dyadic symmetry would benefit most from the properties of Walsh analysis and the computational advantages it offers. Some applications in the areas of Information Theory and Pattern Recognition are demonstrated. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1970
Accession Number
AD0713194

Entities

People

  • Judea Pearl

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Data Science
  • Distribution Functions
  • Harmonic Analysis
  • Information Science
  • Information Theory
  • Pattern Recognition
  • Probability
  • Probability Distribution Functions
  • Probability Distributions
  • Random Variables
  • Recognition
  • Spectra
  • Statistical Analysis
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Parallel and Distributed Computing.
  • Theoretical Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms