Monte Carlo Approximations in Bayesian Decision Theory. Part 1. Revision

Abstract

In decision-making problems, the Bayesian action and its posterior expected loss usually can not be obtained analytically. This paper studies a Monte Carlo method for approximating the Bayesian action and its posterior expected loss. The Monte Carlo approximation to the Bayesian action is obtained through approximating the posterior expected loss function by using the Monte Carlo integration method and searching the minimum of the approximated posterior expected loss function. As the Monte Carlo sample size diverges to infinity, the Monte Carlo approximations are shown to be convergent in very general situations. The rates of the convergence are also obtained under some regularity conditions on the loss function. Two accuracy measures of the Monte Carlo approximations are proposed. Some examples are presented for illustration.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1989
Accession Number
ADA204287

Entities

People

  • Jun Shao

Organizations

  • Purdue University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Accuracy
  • Classification
  • Computations
  • Convergence
  • Data Science
  • Decision Theory
  • Information Science
  • Monte Carlo Method
  • New York
  • Probability Distributions
  • Random Variables
  • Security
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • Surveys
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.

Technology Areas

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