Sampling Based Approaches to Calculating Marginal Densities

Abstract

Stochastic substitution, the Gibbs sampler and the sampling-importance-resampling algorithm can be viewed as three alternative sampling, or Monte Carlo, based approaches to the calculation of numerical estimates of marginal probability distributions. The three approaches will be reviewed, and compared and contrasted, in relation to various joint probability structures frequently encountered in applications. In particular, the relevance of the approaches to calculating Bayesian posterior densities for a variety of structured models will be discussed and illustrated. Keywords: Marginal density; Monte Carlo sampling; Stochastic substitution; Gibbs sampler; Importance sampling; Conditional probability structure; Posterior distributions; Data augmentation; Hierarchical models; Missing data; Variance components.

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Document Details

Document Type
Technical Report
Publication Date
Apr 11, 1989
Accession Number
ADA208388

Entities

People

  • Adrian F. Smith
  • Alan E. Gelfand

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Artificial Intelligence
  • Bayesian Inference
  • Data Science
  • Estimators
  • Information Processing
  • Information Science
  • Maximum Likelihood Estimation
  • Monte Carlo Method
  • Numerical Analysis
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Sampling
  • Statistics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Regression Analysis.

Technology Areas

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