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45
Markov chains for exploring posterior distributions
 Annals of Statistics
, 1994
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Cited by 1131 (6 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Regeneration in Markov Chain Samplers
, 1994
"... Markov chain sampling has received considerable attention in the recent literature, in particular in the context of Bayesian computation and maximum likelihood estimation. This paper discusses the use of Markov chain splitting, originally developed as a tool for the theoretical analysis of general s ..."
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Cited by 109 (5 self)
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Markov chain sampling has received considerable attention in the recent literature, in particular in the context of Bayesian computation and maximum likelihood estimation. This paper discusses the use of Markov chain splitting, originally developed as a tool for the theoretical analysis of general state space Markov chains, to introduce regeneration times into Markov chain samplers. This allows the use of regenerative methods for analyzing the output of these samplers, and can also provide a useful diagnostic of the performance of the samplers. The general approach is applied to several different samplers and is illustrated in a number of examples. 1 Introduction In Markov chain Monte Carlo, a distribution ß is examined by obtaining sample paths from a Markov chain constructed to have equilibrium distribution ß. This approach was introduced by Metropolis et al. (1953) and has recently received considerable attention as a method for examining posterior distributions in Bayesian infer...
Exact sampling from a continuous state space, Scandinavian
 Journal of Statistics
, 1998
"... ABSTRACT. Propp & Wilson (1996) described a protocol, called coupling from the past, for exact sampling from a target distribution using a coupled Markov chain Monte Carlo algorithm. In this paper we extend coupling from the past to various MCMC samplers on a continuous state space; rather than ..."
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Cited by 102 (7 self)
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ABSTRACT. Propp & Wilson (1996) described a protocol, called coupling from the past, for exact sampling from a target distribution using a coupled Markov chain Monte Carlo algorithm. In this paper we extend coupling from the past to various MCMC samplers on a continuous state space; rather than following the monotone sampling device of Propp & Wilson, our approach uses methods related to gammacoupling and rejection sampling to simulate the chain, and direct accounting of sample paths.
Two Estimators of the Mean of a Counting Process with Panel Count Data
, 1998
"... We study two estimators of the mean function of a counting process based on "panel count data". The setting for "panel count data" is one in which n independent subjects, each with a counting process with common mean function, are observed at several possibly di erent times durin ..."
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Cited by 32 (13 self)
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We study two estimators of the mean function of a counting process based on "panel count data". The setting for "panel count data" is one in which n independent subjects, each with a counting process with common mean function, are observed at several possibly di erent times during a study. Following a model proposed by Schick and Yu (1997), we allow the number of observation times, and the observation times themselves, to be random variables. Our goal is to estimate the mean function of the counting process. We show that the estimator of the mean function proposed by Sun and Kalbfleisch (1995) can be viewed as a pseudomaximum likelihood estimator when a nonhomogeneous Poisson process model is assumed for the counting process. We establish consistency of both the nonparametric pseudo maximum likelihood estimator of Sun and Kalbfleisch (1995) and the full maximum likelihood estimator, even if the underlying counting process is not a Poisson process. We also derive the asymptotic distribution of both estimators at a xed time t, and compare the resulting theoretical relative e ciency with nite sample relative efficiency by way of a limited montecarlo study.
Two likelihoodbased semiparametric estimation methods for panel count data with covariates
, 2005
"... We consider estimation in a particular semiparametric regression model for the mean of a counting process with “panel count ” data. The basic model assumption is that the conditional mean function of the counting process is of the form E{N(t)Z} = exp(β T 0 Z)Λ0(t) where Z is a vector of covariates ..."
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Cited by 25 (7 self)
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We consider estimation in a particular semiparametric regression model for the mean of a counting process with “panel count ” data. The basic model assumption is that the conditional mean function of the counting process is of the form E{N(t)Z} = exp(β T 0 Z)Λ0(t) where Z is a vector of covariates and Λ0 is the baseline mean function. The “panel count ” observation scheme involves observation of the counting process N for an individual at a random number K of random time points; both the number and the locations of these time points may differ across individuals. We study semiparametric maximum pseudolikelihood and maximum likelihood estimators of the unknown parameters (β0,Λ0) derived on the basis of a nonhomogeneous Poisson process assumption. The pseudolikelihood estimator is fairly easy to compute, while the maximum likelihood estimator poses more challenges from the computational perspective. We study asymptotic properties of both estimators assuming that the proportional mean model holds, but dropping the Poisson process assumption used to derive the estimators. In particular we establish asymptotic normality for the estimators of the regression parameter β0 under appropriate hypotheses. The results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process.
An Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis
 Statistics and Computing
, 1991
"... The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rej ..."
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The Gibbs sampler has been proposed as a general method for Bayesian calculation in Gelfand and Smith (1990). However, the predominance of experience to date resides in applications assuming conjugacy where implementation is reasonably straightforward. This paper describes a tailored approximate rejection method approach for implementation of the Gibbs sampler when nonconjugate structure is present. Several challenging applications are presented for illustration.
Bayesian and Frequentist Approaches to Parametric Predictive Inference
 BAYESIAN STATISTICS, J. M. BERNARDO , J. O. BERGER , A. P. DAWID , A. F. M. SMITH (EDS.)
, 1998
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Consistency of Markov chain quasiMonte Carlo on continuous state
, 2009
"... The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [31] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The pr ..."
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Cited by 14 (4 self)
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The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [31] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than IID U(0, 1) points shows consistency for estimated means, but only applies for discrete stationary distributions. We extend those results to some MCMC algorithms for continuous stationary distributions. The main motivation is the search for quasiMonte Carlo versions of MCMC. As a side benefit, the results also establish consistency for the usual method of using pseudorandom numbers in place of random ones. 1
Riemann Sums for MCMC Estimation and Convergence Monitoring
"... This paper develops an extension of the Riemann sum techniques of Philippe (1997b) in the setup of MCMC algorithms. It shows that the technique applies equally well to the output of these algorithms, with similar speeds of convergence which improve upon the regular estimator. The restriction on the ..."
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Cited by 5 (0 self)
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This paper develops an extension of the Riemann sum techniques of Philippe (1997b) in the setup of MCMC algorithms. It shows that the technique applies equally well to the output of these algorithms, with similar speeds of convergence which improve upon the regular estimator. The restriction on the dimension associated with Riemann sums can furthermore be overcome by RaoBlackwellization methods. This approach can also be used as a control variate technique in convergence assessment of MCMC algorithms, either by comparing the values of alternative versions of Riemann sums, which estimate a same quantity, or by using genuine control variate, that is, functions with know expectations, which are available in full generality for constants and scores. Keywords: simulation, numerical integration, control variate, Rao Blackwellization, score. This work was partially supported by the TMR network, contract C.E. CT 960095. The authors are grateful to Steve Brooks for helpful discussions about...