On a likelihood approach for Monte Carlo integration

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60 Scopus citations


The use of estimating equations has been a common approach for constructing Monte Carlo estimators. Recently, Kong et al. proposed a formulation of Monte Carlo integration as a statistical model, making explicit what information is ignored and what is retained about the baseline measure. From simulated data, the baseline measure is estimated by maximum likelihood, and then integrals of interest are estimated by substituting the estimated measure. For two different situations in which independent observations are simulated from multiple distributions, we show that this likelihood approach achieves the lowest asymptotic variance possible by using estimating equations. In the first situation, the normalizing constants of the design distributions are estimated, and Meng and Wong's bridge sampling estimating equation is considered. In the second situation, the values of the normalizing constants are known, thereby imposing linear constraints on the baseline measure. Estimating equations including Hesterberg's stratified importance sampling estimator. Veach and Guibas's multiple importance sampling estimator, and Owen and Zhou's method of control variates are considered.

Original languageEnglish (US)
Pages (from-to)1027-1036
Number of pages10
JournalJournal of the American Statistical Association
Issue number468
StatePublished - Dec 2004
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Bridge sampling
  • Control variate
  • Importance sampling
  • Stratified sampling


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