Empirical Bayes Estimation of Proportions in Several Groups.

Abstract

The problem of estimating binomial proportions in several similar but not necessarily identical groups occurs frequently in psychological and educational settings. A straightforward empirical Bayes approach to this problem using a slight extension of the standard Bayesian method for estimating a single proportion is proposed. Novick, Lewis, and Jackson (1973) suggest a purely Bayesian solution to the problem which uses a root arcsine transformation of the proportions. They contrast their method with a similar approach using the same transformation, due to Jackson (1972) using examples to show that the Bayesian approach is better. This note shows that an improved version of Jackson's approach yields much more satisfactory results than the original, so the advantage of the purely Bayesian approach is questionable. But the revised version of Jackson's approach and the new beta-binomial approach yield practically identical results, so even the need for using the root-arcsine transformation is questionable, except when the proportions are concentrated near zero or one.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1981
Accession Number
ADA118667

Entities

People

  • James A. Paulson

Organizations

  • Portland State University

Tags

Communities of Interest

  • Biomedical
  • Human Systems

DTIC Thesaurus Topics

  • Air Force
  • Analysis Of Variance
  • Bayesian Networks
  • Computational Complexity
  • Computational Science
  • Data Science
  • Educational Psychology
  • Equations
  • Estimators
  • Information Science
  • Manpower Utilization
  • Military Research
  • Personnel Management
  • Probability
  • Probability Distributions
  • Psychology
  • Standards

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.

Technology Areas

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