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On the Convergence of Monte Carlo Maximum Likelihood Calculations
 Journal of the Royal Statistical Society B
, 1992
"... Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the ..."
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Cited by 59 (3 self)
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Monte Carlo maximum likelihood for normalized families of distributions (Geyer and Thompson, 1992) can be used for an extremely broad class of models. Given any family f h ` : ` 2 \Theta g of nonnegative integrable functions, maximum likelihood estimates in the family obtained by normalizing the the functions to integrate to one can be approximated by Monte Carlo, the only regularity conditions being a compactification of the parameter space such that the the evaluation maps ` 7! h ` (x) remain continuous. Then with probability one the Monte Carlo approximant to the log likelihood hypoconverges to the exact log likelihood, its maximizer converges to the exact maximum likelihood estimate, approximations to profile likelihoods hypoconverge to the exact profile, and level sets of the approximate likelihood (support regions) converge to the exact sets (in Painlev'eKuratowski set convergence). The same results hold when there are missing data (Thompson and Guo, 1991, Gelfand and Carlin, 19...
Estimating Normalizing Constants and Reweighting Mixtures in Markov Chain Monte Carlo
, 1994
"... Markov chain Monte Carlo (the MetropolisHastings algorithm and the Gibbs sampler) is a general multivariate simulation method that permits sampling from any stochastic process whose density is known up to a constant of proportionality. It has recently received much attention as a method of carrying ..."
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Cited by 40 (0 self)
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Markov chain Monte Carlo (the MetropolisHastings algorithm and the Gibbs sampler) is a general multivariate simulation method that permits sampling from any stochastic process whose density is known up to a constant of proportionality. It has recently received much attention as a method of carrying out Bayesian, likelihood, and frequentist inference in analytically intractable problems. Although many applications of Markov chain Monte Carlo do not need estimation of normalizing constants, three do: calculation of Bayes factors, calculation of likelihoods in the presence of missing data, and importance sampling from mixtures. Here reverse logistic regression is proposed as a solution to the problem of estimating normalizing constants, and convergence and asymptotic normality of the estimates are proved under very weak regularity conditions. Markov chain Monte Carlo is most useful when combined with importance reweighting so that a Monte Carlo sample from one distribution can be used fo...
Discussion of the paper "Markov chains for exploring posterior distributions" by Luke Tierney
 Leipzig und Berlin
, 1994
"... this paper, which even before its appearance has done a valuable service in clarifying both theory and practice in this important area. For example, the discussion of combining strategies in Section 2.4 helped researchers break away from pure Gibbs sampling in 1991; it was, for example, part of the ..."
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Cited by 3 (0 self)
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this paper, which even before its appearance has done a valuable service in clarifying both theory and practice in this important area. For example, the discussion of combining strategies in Section 2.4 helped researchers break away from pure Gibbs sampling in 1991; it was, for example, part of the reasoning that lead to the "Metropoliscoupled" scheme of Geyer (1991) mentioned at the end of Section 2.3.3.