Maximum Likelihood Estimation for Constrained or Missing Data Models

Abstract

In statistical models involving constrained or missing data, likelihoods constrained integrals emerge. In the case of both constrained and missing data, the result is a ratio of integrals, which for multivariate data may defy exact or approximate analytic expression. Seeking maximum likelihood estimates in such setting, we propose Monte Carlo approximants for these integrals, and subsequently maximize the resulting approximate likelihood. Iteration of this strategy expedites the maximization, while the Gibbs sampler is useful for the required Monte Carlo generation. As a result, we handle a class of models broader than the customary EM setting without using an EM-type algorithm. Implementation of the methodology is illustrated in two numerical examples. EM Algorithm, Gibbs sampler, Monte Carlo approximant.

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Document Details

Document Type
Technical Report
Publication Date
May 05, 1993
Accession Number
ADA266563

Entities

People

  • Alan E. Gelfand
  • Bradley P. Carlin

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Bayesian Networks
  • Computational Science
  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Maximum Likelihood Estimation
  • Monte Carlo Method
  • New York
  • Sampling
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.