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178
Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review
 Journal of the American Statistical Association
, 1996
"... A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise ..."
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Cited by 223 (6 self)
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A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but currently has yielded relatively little that is of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of thirteen convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all the methods can fail to detect the sorts of convergence failure they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler conver...
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.
MCMC Analysis of Diffusion Models with Application to Finance
 Journal of Business and Economic Statistics
, 1998
"... This paper proposes a new method for estimation of parameters in diffusion processes from ..."
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Cited by 88 (3 self)
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This paper proposes a new method for estimation of parameters in diffusion processes from
Sequential Monte Carlo Methods for Multiple Target Tracking and Data Fusion
 IEEE Trans. on Signal Processing
, 2002
"... Abstract—The classical particle filter deals with the estimation of one state process conditioned on a realization of one observation process. We extend it here to the estimation of multiple state processes given realizations of several kinds of observation processes. The new algorithm is used to tr ..."
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Cited by 78 (5 self)
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Abstract—The classical particle filter deals with the estimation of one state process conditioned on a realization of one observation process. We extend it here to the estimation of multiple state processes given realizations of several kinds of observation processes. The new algorithm is used to track with success multiple targets in a bearingsonly context, whereas a JPDAF diverges. Making use of the ability of the particle filter to mix different types of observations, we then investigate how to join passive and active measurements for improved tracking. Index Terms—Bayesian estimation, bearingsonly tracking, Gibbs sampler, multiple receivers, multiple targets tracking,
Tracking Multiple Objects with Particle Filtering
, 2000
"... We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the ..."
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Cited by 75 (4 self)
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We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the multiple targets. We propose an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler. This algorithm is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem. Moreover this algorithm is easily extended to multireceiver observations where the receivers can produce measurements of various nature with different frequencies.
Variable Selection for Regression Models
, 1998
"... A simple method for subset selection of independent variables in regression models is proposed. We expand the usual regression equation to an equation that incorporates all possible subsets of predictors by adding indicator variables as parameters. The vector of indicator variables dictates which pr ..."
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Cited by 41 (2 self)
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A simple method for subset selection of independent variables in regression models is proposed. We expand the usual regression equation to an equation that incorporates all possible subsets of predictors by adding indicator variables as parameters. The vector of indicator variables dictates which predictors to include. Several choices of priors can be employed for the unknown regression coefficients and the unknown indicator parameters. The posterior distribution of the indicator vector is approximated by means of the Markov chain Monte Carlo algorithm. We select subsets with high posterior probabilities. In addition to linear models, we consider generalized linear models.
Biclustering microarray data by Gibbs sampling
 Bioinformatics
, 2003
"... Motivation: Gibbs sampling has become a method of choice for the discovery of noisy patterns, known as motifs, in DNA and protein sequences. Because handling noise in microarray data presents similar challenges, we have adapted this strategy to the biclustering of discretized microarray data. ..."
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Cited by 32 (3 self)
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Motivation: Gibbs sampling has become a method of choice for the discovery of noisy patterns, known as motifs, in DNA and protein sequences. Because handling noise in microarray data presents similar challenges, we have adapted this strategy to the biclustering of discretized microarray data.
Bayesian Estimation and Testing of Structural Equation Models
 Psychometrika
, 1999
"... The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameter ..."
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Cited by 27 (8 self)
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The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errorsinvariables model.