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Markov Chain Monte Carlo Simulation Methods in Econometrics
, 1993
"... We present several Markov chain Monte Carlo simulation methods that have been widely used in recent years in econometrics and statistics. Among these is the Gibbs sampler, which has been of particular interest to econometricians. Although the paper summarizes some of the relevant theoretical literat ..."
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Cited by 91 (5 self)
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We present several Markov chain Monte Carlo simulation methods that have been widely used in recent years in econometrics and statistics. Among these is the Gibbs sampler, which has been of particular interest to econometricians. Although the paper summarizes some of the relevant theoretical literature, its emphasis is on the presentation and explanation of applications to important models that are studied in econometrics. We include a discussion of some implementation issues, the use of the methods in connection with the EM algorithm, and how the methods can be helpful in model specification questions. Many of the applications of these methods are of particular interest to Bayesians, but we also point out ways in which frequentist statisticians may find the techniques useful.
A survey of Monte Carlo algorithms for maximizing the likelihood of a twostage hierarchical model
, 2001
"... Likelihood inference with hierarchical models is often complicated by the fact that the likelihood function involves intractable integrals. Numerical integration (e.g. quadrature) is an option if the dimension of the integral is low but quickly becomes unreliable as the dimension grows. An alternati ..."
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Cited by 10 (4 self)
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Likelihood inference with hierarchical models is often complicated by the fact that the likelihood function involves intractable integrals. Numerical integration (e.g. quadrature) is an option if the dimension of the integral is low but quickly becomes unreliable as the dimension grows. An alternative approach is to approximate the intractable integrals using Monte Carlo averages. Several dierent algorithms based on this idea have been proposed. In this paper we discuss the relative merits of simulated maximum likelihood, Monte Carlo EM, Monte Carlo NewtonRaphson and stochastic approximation. Key words and phrases : Eciency, Monte Carlo EM, Monte Carlo NewtonRaphson, Rate of convergence, Simulated maximum likelihood, Stochastic approximation All three authors partially supported by NSF Grant DMS0072827. 1 1
Hierarchical Models: A Current Computational Perspective
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2000
"... Hierarchical models (HMs) provide a flexible framework for modeling data. The ongoing development of techniques like the EM algorithm and Markov chain Monte Carlo has enabled statisticians to make use of increasingly more complicated HMs over the last few decades. In this article, we consider Bay ..."
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Cited by 9 (1 self)
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Hierarchical models (HMs) provide a flexible framework for modeling data. The ongoing development of techniques like the EM algorithm and Markov chain Monte Carlo has enabled statisticians to make use of increasingly more complicated HMs over the last few decades. In this article, we consider Bayesian and frequentist versions of a general, twostage HM, and describe several examples from the literature that illustrate its versatility. Some key aspects of the computational techniques that are currently used in conjunction with this HM are then examined in the context of McCullagh and Nelder's (1989) salamander data. Several areas that are ripe for new research are identified.
61, Part 2, pp. 381^400 Inference in generalized additive mixed models by using smoothing splines
, 1997
"... Summary. Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows ¯exible functional dependence of an outcome variable on covariates by using nonparametri ..."
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Summary. Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows ¯exible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasilikelihood. Because numerical integration is often required by maximizing the objective functions, double penalized quasilikelihood is proposed to make approximate inference. Frequentist and Bayesian inferences are compared. A key feature of the method proposed is that it allows us to make systematic inference on all model components within a uni®ed parametric mixed model framework and can be easily implemented by ®tting a working generalized linear mixed model by using existing statistical software. A bias correction procedure is also proposed to improve the performance of double penalized quasilikelihood for sparse data. We illustrate the method with an application to infectious disease data and we evaluate its performance through simulation.