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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...
Markov Chain Monte Carlo for Statistical Inference
 University of Washington, Center for
, 2000
"... These notes provide an introduction to Markov chain Monte Carlo methods that are useful in both Bayesian and frequent... ..."
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Cited by 18 (0 self)
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These notes provide an introduction to Markov chain Monte Carlo methods that are useful in both Bayesian and frequent...
Markov chain Monte Carlo methods for statistical inference
, 2004
"... These notes provide an introduction to Markov chain Monte Carlo methods and their applications to both Bayesian and frequentist statistical inference. Such methods have revolutionized what can be achieved computationally, especially in the Bayesian paradigm. The account begins by discussing ordinary ..."
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Cited by 7 (0 self)
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These notes provide an introduction to Markov chain Monte Carlo methods and their applications to both Bayesian and frequentist statistical inference. Such methods have revolutionized what can be achieved computationally, especially in the Bayesian paradigm. The account begins by discussing ordinary Monte Carlo methods: these have the same goals as the Markov chain versions but can only rarely be implemented. Subsequent sections describe basic Markov chain Monte Carlo, based on the Hastings algorithm and including both the Metropolis method and the Gibbs sampler as special cases, and go on to discuss some more specialized developments, including adaptive slice sampling, exact goodness–of–fit tests, maximum likelihood estimation, the Langevin–Hastings algorithm, auxiliary variables techniques, perfect sampling via coupling from the past, reversible jumps methods for target spaces of varying dimensions, and simulated annealing. Specimen applications are described throughout the notes.
Geographic exposure modeling: a valuable extension of geographic information systems use for environmental epidemiology. Environ Health Perspect 107:181–190
, 1999
"... Geographic modeling of individual exposures using air pollution modeling techniques can help in both the design of environmental epidemiologic studies and in the assignment of measures that delineate regions that receive the highest exposure in space and time. Geographic modeling can help in the int ..."
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Cited by 5 (0 self)
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Geographic modeling of individual exposures using air pollution modeling techniques can help in both the design of environmental epidemiologic studies and in the assignment of measures that delineate regions that receive the highest exposure in space and time. Geographic modeling can help in the interpretation of environmental sampling data associated with airborne concentration or deposition, and can act as a sophisticated interpolator for such data, allowing values to be assigned to locations between points where the data have actually been collected. Recent advances allow for quantification of the uncertainty in a geographic model and the resulting impact on estimates of association, variability, and study power. In this paper we present the terminology and methodology of geographic modeling, describe applications to date in the field of epidemiology, and evaluate the potential of this relatively new tool. Environ Health Perspect 1 07(Suppl 1):181190 (1999).
MONTE CARLO LIKELIHOOD INFERENCE FOR MISSING DATA MODELS
"... We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are independent and identically distributed and independent of the observe ..."
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Cited by 4 (2 self)
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We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are independent and identically distributed and independent of the observed data. Our Monte Carlo approximation to the MLE is a consistent and asymptotically normal estimate of the minimizer θ ∗ of the KullbackLeibler information, as both Monte Carlo and observed data sample sizes go to infinity simultaneously. Plugin estimates of the asymptotic variance are provided for constructing confidence regions for θ ∗. We give LogitNormal generalized linear mixed model examples, calculated using an R package. AMS 2000 subject classifications. Primary 62F12; secondary 65C05. Key words and phrases. Asymptotic theory, Monte Carlo, maximum likelihood, generalized
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.
Multipoint linkage analyses for disease mapping in extended pedigrees: A Markov chain Monte Carlo approach
, 2002
"... Multipoint linkage analyses ofgenetic data on extended pedigrees can involve exact computations which are infeasible. Markov chain Monte Carlo methods represent an attractive alternative, greatly extending the range of models and data sets for which analysis is practical. In this paper, several adva ..."
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Cited by 1 (1 self)
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Multipoint linkage analyses ofgenetic data on extended pedigrees can involve exact computations which are infeasible. Markov chain Monte Carlo methods represent an attractive alternative, greatly extending the range of models and data sets for which analysis is practical. In this paper, several advances in Markov chain Monte Carlo theory, namely joint updates of latent variables across loci and meioses, integrated proposals, MetropolisHastings restarts via sequential imputation and Rao Blackwellized estimators, are incorporated into a sampling strategy which mixes well and produces accurate results in real time. The methodology is demonstrated through its application to several data sets originating from a study of earlyonset Alzheimer's disease in families of VolgaGerman ethnic origin.
Open Access
"... Reconstructing CNV genotypes using segregation analysis: combining pedigree information with CNV assay ..."
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Reconstructing CNV genotypes using segregation analysis: combining pedigree information with CNV assay
Model Based Clustering for Longitudinal Data
, 2007
"... A modelbased clustering method is proposed for clustering individuals on the basis of measurements taken over time. Data variability is taken into account through nonlinear hierarchical models leading to a mixture of hierarchical models. We study both frequentist and Bayesian estimation procedures ..."
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A modelbased clustering method is proposed for clustering individuals on the basis of measurements taken over time. Data variability is taken into account through nonlinear hierarchical models leading to a mixture of hierarchical models. We study both frequentist and Bayesian estimation procedures. From a classical viewpoint, we discuss maximum likelihood estimation of this family of models through the EM algorithm. From a Bayesian standpoint, we develop appropriate Markov chain Monte Carlo (MCMC) sampling schemes for the exploration of target posterior distribution of parameters. The methods are illustrated with the identification of hormone trajectories that are likely to lead to adverse pregnancy outcomes in a group of pregnant women.