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17
Markov chains for exploring posterior distributions
 Annals of Statistics
, 1994
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Cited by 753 (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
Adaptive Markov Chain Monte Carlo through Regeneration
, 1998
"... this paper is organized as follows. In Section 2 we introduce the concept of regeneration and adaptation at regeneration, and provide theoretical support. In Section 3, the splitting techniques required for adaptation are reviewed. Section 4 contains four illustrations of adaptive MCMC. Some of the ..."
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Cited by 71 (4 self)
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this paper is organized as follows. In Section 2 we introduce the concept of regeneration and adaptation at regeneration, and provide theoretical support. In Section 3, the splitting techniques required for adaptation are reviewed. Section 4 contains four illustrations of adaptive MCMC. Some of the proofs from Sections 2 and 3 are placed in the Appendix. 2 Regeneration: A Framework for Adaptation
Identification of regeneration times in MCMC simulation, with application to adaptive schemes
 Journal of Computational and Graphical Statistics
, 2005
"... Regeneration is a useful tool in Markov chain Monte Carlo simulation, since it can be used to sidestep the burnin problem and to construct better estimates of the variance of parameter estimates themselves. It also provides a simple way to introduce adaptive behaviour into a Markov chain, and to ..."
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Cited by 19 (2 self)
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Regeneration is a useful tool in Markov chain Monte Carlo simulation, since it can be used to sidestep the burnin problem and to construct better estimates of the variance of parameter estimates themselves. It also provides a simple way to introduce adaptive behaviour into a Markov chain, and to use parallel processors to build a single chain. Regeneration is often difficult to take advantage of, since for most chains, no recurrent proper atom exists, and it is not always easy to use Nummelin’s splitting method to identify regeneration times. This paper describes a constructive method for generating a Markov chain with a specified target distribution and identifying regeneration times. As a special case of the method, an algorithm which can be “wrapped ” around an existing Markov transition kernel is given. In addition, a specific rule for adapting the transition kernel at regeneration times is introduced, which gradually replaces the original transition kernel with an independencesampling MetropolisHastings kernel using a mixture normal approximation to the target density as its proposal density. Computational gains for the regenerative adaptive algorithm are demonstrated in examples.
Alternatives to the Gibbs Sampling Scheme
, 1992
"... A variation of the Gibbs sampling scheme is defined by driving the simulated Markov chain by the conditional distributions of an approximation to the posterior rather than the posterior distribution itself. Choosing a multivariate normal mixture form for the approximation enables reparametrization w ..."
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Cited by 6 (1 self)
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A variation of the Gibbs sampling scheme is defined by driving the simulated Markov chain by the conditional distributions of an approximation to the posterior rather than the posterior distribution itself. Choosing a multivariate normal mixture form for the approximation enables reparametrization which is crucial to improve convergence in the Gibbs sampler. Using an approximation to the posterior density also opens the possiblity to include a learning process about the  in the operational sense of evaluating posterior integrals  unknown posterior density in the algorithm. While ideally this should be done using available pointwise evaluations of the posterior density, this is too difficult in a general framework and we use instead the currently available Monte Carlo sample to adjust the approximating density. This is done using a simple multivariate implementation of the mixture of Dirichlet density estimation algorithm. Keywords: Markov chain Monte Carlo, Bayesian sampling, stocha...
Bayesian Analysis of Ordered Categorical Data from Industrial Experiments
 Technometrics
, 1995
"... Data from industrial experiments often involve an ordered categorical response, such as a qualitative rating. ANOVA based analyses may be inappropriate for such data, suggesting the use of Generalized Linear Models (GLMs). When the data are observed from a fractionated experiment, likelihoodbas ..."
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Cited by 5 (1 self)
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Data from industrial experiments often involve an ordered categorical response, such as a qualitative rating. ANOVA based analyses may be inappropriate for such data, suggesting the use of Generalized Linear Models (GLMs). When the data are observed from a fractionated experiment, likelihoodbased GLM estimates may be innite, especially when factors have large eects. These diculties are overcome with a Bayesian GLM, which is implemented via the Gibbs sampling algorithm. Techniques for modeling data and for subsequently using the identied model to optimize the process are outlined. An important advantage in the optimization stage is that uncertainty in the parameter estimates is accounted for in the model. For robust design experiments, the Bayesian approach easily incorporates the variability of the noise factors using the response modeling approach (Welch, Yu, Kang and Sacks 1990 and Shoemaker, Tsui and Wu 1991). This approach and its techniques are used to analyze two...
Metropolis Based Posterior Integration Schemes
 Numerical Recipes in Fortran (2nd Edition
, 1994
"... This paper proposes a Metropolis based algorithm to generate posterior Monte Carlo samples. The algorithm does not directly depend upon any approximation or envelope function for the posterior density. Convergence in total variation and an ergodic theorem are shown. Applying the proposed scheme to g ..."
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Cited by 3 (1 self)
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This paper proposes a Metropolis based algorithm to generate posterior Monte Carlo samples. The algorithm does not directly depend upon any approximation or envelope function for the posterior density. Convergence in total variation and an ergodic theorem are shown. Applying the proposed scheme to generate from the conditional distributions required for the Gibbs sampler extends the applicability of the Gibbs sampling scheme to problems without conjugate structure and makes orthogonalization possible. Orthogonalization improves the convergence of the Gibbs sampler by reducing serial correlation. The proposed algorithms nicely complement available posterior integration schemes. Most currently used posterior integration techniques rely on approximate posterior normality (importance sampling, Laplace integration) or complete conditionals of the posterior distribution which are available for efficient random variate generation (Gibbs sampling). The suggested algorithms rely to a much lesse...
Adaptation for Self Regenerative MCMC
, 1998
"... this article we provide a generic adaptation scheme for the above algorithm. The adaptive scheme is to use the knowledge of the stationary distribution gathered so far and then to update / during the course of the simulation. This method is easy to implement and often leads to considerable improveme ..."
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Cited by 2 (0 self)
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this article we provide a generic adaptation scheme for the above algorithm. The adaptive scheme is to use the knowledge of the stationary distribution gathered so far and then to update / during the course of the simulation. This method is easy to implement and often leads to considerable improvement. We obtain theoretical results for the adaptive scheme. Our proposed methodology is illustrated with a number of realistic examples in Bayesian computation and its performance is compared with other available MCMC techniques. In one of our applications we develop a nonlinear dynamics model for modeling predatorprey relationships in the wild.
BUGS 0.6 Bayesian inference using Gibbs sampling (addendum to manual
 Medical Research Council Biostatistics Unit, Institute of Public Health
, 1997
"... This Addendum speci es additional features of BUGS 0.6, and should be read in conjunction with the current manual for BUGS 0.5 (Spiegelhalter et al., 1996a). Contents 1 Getting started 2 1.1 Getting the software.................................... 2 1.2 The script le for `bugs ' (Sparc)............. ..."
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Cited by 2 (0 self)
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This Addendum speci es additional features of BUGS 0.6, and should be read in conjunction with the current manual for BUGS 0.5 (Spiegelhalter et al., 1996a). Contents 1 Getting started 2 1.1 Getting the software.................................... 2 1.2 The script le for `bugs ' (Sparc)............................. 2
Smooth Transition Garch Models: A Bayesian Perspective
, 1998
"... This paper proposes a new kind of asymmetric GARCH where the conditional variance obeys two di#erent regimes with a smooth transition function. In one formulation, the conditional variance reacts di#erently to negative and positive shocks while in a second formulation, small and big shocks have sepa ..."
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Cited by 1 (1 self)
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This paper proposes a new kind of asymmetric GARCH where the conditional variance obeys two di#erent regimes with a smooth transition function. In one formulation, the conditional variance reacts di#erently to negative and positive shocks while in a second formulation, small and big shocks have separate e#ects. The introduction of a threshold allows for a mixed e#ect. A Bayesian strategy, based on the comparison between posterior and predictiveBayesian residuals, is built for detecting the presence and the shape of nonlinearities. The method is applied to the Brussels and Tokyo stock indexes. The need for an alternative parameterisation of the GARCH model is emphasised as a solution to numerical problems. Keywords: Bayesian, asymmetric GARCH, speci#cation tests, nonlinear modelling, stock indexes. JEL classi#cation: C11, C22, C51, G14. 1 GREQAMCNRS, 2 rue de la Charit#e, 13002 Marseille, France and CORE, 34 voie du Roman Pays, B1348 Louvain la Neuve, Belgique. email: lubrano@ehess.cnrsmrs.fr The basic idea of this paper #smooth transition GARCH# grew out during the visit of Timo Terasvirta at GREQAM in September 1996. Once a #rst version of this paper was completed and presented at EC 2 , Florence December 1996, it appeared that a similar e#ort has been pursued in a classical framework by GonzalesRiviera #1996# and byby Hagerud #1997#. Some of the ideas concerning the reparameterisation of GARCH models have been explored in discussions with Rob Engle during his visit in Marseille in June 1992, conversations later pursued with JeanFran #cois Richard. I am grateful to participants of seminars in Marseille, Bordeaux, Louvain, Maastricht, to participants to the conference EC2 #Simulation Methods in Econometrics" held in Florence, December 1996, to the KrakowWorksh...
BUGS*Examples  Version 0.5 Volume 2
, 1996
"... Introduction and Disclaimer These worked examples illustrate the use of the BUGS language and sampler in a wide range of problems. They contain a number of useful "tricks", but are certainly not exhaustive of the models that may be analysed. We emphasise that all the results for these examples have ..."
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Introduction and Disclaimer These worked examples illustrate the use of the BUGS language and sampler in a wide range of problems. They contain a number of useful "tricks", but are certainly not exhaustive of the models that may be analysed. We emphasise that all the results for these examples have been derived in the most naive way: in general a burnin of 500 iterations and a single long run of 1000 iterations. This is not recommended as a general technique: no tests of convergence have been carried out, and traces of the estimates have not even been plotted. However, comparisons with published results have been made where possible. Times have been measured on a 60 MHz superSPARC: a 60 MHz Pentium PC appears to be about 4 times slower, and a 30 MHz superSPARC about 2 times slower. Users are warned to be extremely careful about assuming convergence, especially when using complex models including errors in variables, crossed random effects and intrinsic p