A Bayes Rule for Selecting the Largest Component.

Abstract

Let X subscript bar = (X subscript 1,...,X subscript k) be a random vector whose distribution depends on an unknown vector parameter theta subscript bar = (theta subscript 1, theta subscript k). The marginal distribution of X subscript i depends on theta subscript i only, i = 1,...,k. This paper deals with the problem of selecting the largest component of theta subscript bar and the analogous problem of selecting a subset of the components of theta subscript bar which includes the largest component. We consider the selection problem in a general decision theoretic framework and derive Bayes rules for selecting the largest component. The Bayes rules are shown to have certain optimal properties. The ordinary selection rules are shown to be Bayes rules, with respect to a special loss function. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 16, 1981
Accession Number
ADA112946

Entities

People

  • Khursheed Alam

Organizations

  • Clemson University

Tags

DTIC Thesaurus Topics

  • Bayesian Networks
  • Contracts
  • Covariance
  • Identities
  • Inequalities
  • Literature
  • Military Research
  • Normal Distribution
  • Probabilistic Models
  • Probability
  • Probability Distributions
  • Specifications
  • Standards
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.
  • Statistical inference.

Technology Areas

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