A major stumbling block in multivariate discrete data analysis is the problem of evaluating the outcome probabilities that enter the likelihood function. Calculation of these probabilities involves high-dimensional integration, which has made simulation methods indispensable in both maximum likelihood estimation and Bayesian and frequentist model choice. We review several existing probability estimators and then show that a broader perspective on the simulation problem can be afforded by

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... eting the outcome probabilities through Bayes' theorem, leading to the recognition that estimation can alternatively be handled by Markov chain Monte Carlo (MCMC) methods designed for marginal likelihood computation in Bayesian econometrics. These techniques offer stand-alone approaches to simulated likelihood estimation, but can also be integrated with traditional estimators. Building on both branches in the literature, we develop and discuss new methods that aim to improve efficiency and extend context-specific applicability. A simulation study illustrates the practical benefits and costs associated with each approach. The methods are employed to estimate the likelihood function of a correlated random effects panel data model of women's labor force participation.