Journal ArticleDOI
Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review
TLDR
All of the methods in this work can fail to detect the sorts of convergence failure that they were designed to identify, so a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence are recommended.Abstract:
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 to date has yielded relatively little 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 13 convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler convergence, including ap...read more
Citations
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Journal ArticleDOI
A Bayesian analysis of the multinomial probit model using marginal data augmentation
Kosuke Imai,David A. van Dyk +1 more
TL;DR: A set of new Markov chain Monte Carlo algorithms for Bayesian analysis of the multinomial probit model are introduced, which are as quick to converge as the fastest methods but with a more attractive prior.
Journal ArticleDOI
Estimating parameters in stochastic compartmental models using Markov chain methods
Gavin J. Gibson,Eric Renshaw +1 more
TL;DR: Markov chain Monte Carlo methodology is presented for estimating parameters in stochastic compartmental models from incomplete observations of the corresponding Markov process and it is shown that the methods can be used to provide meaningful estimates of parameters and parameter uncertainty.
Journal ArticleDOI
Inversion of terrestrial ecosystem model parameter values against eddy covariance measurements by Monte Carlo sampling
Wolfgang Knorr,Jens Kattge +1 more
TL;DR: In this article, the authors use a well-known stochastic inversion technique originally developed in nuclear physics, the Metropolis algorithm, to determine the full probability density functions (PDFs) of parameters of a terrestrial ecosystem model.
Journal ArticleDOI
Separation of Non-Negative Mixture of Non-Negative Sources Using a Bayesian Approach and MCMC Sampling
TL;DR: A Markov chain Monte Carlo (MCMC) sampling procedure is proposed to simulate the resulting joint posterior density from which marginal posterior mean estimates of the source signals and mixing coefficients are obtained.
Journal ArticleDOI
Hydrological modelling of the Chaohe Basin in China: Statistical model formulation and Bayesian inference
TL;DR: In this paper, the authors developed a procedure to overcome the problem of non-identifiability of distributed parameters by introducing aggregate parameters and using Bayesian inference, and they demonstrated the good performance of this approach to uncertainty analysis, particularly with respect to the fulfilment of statistical assumptions of the error model.
References
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Journal ArticleDOI
Equation of state calculations by fast computing machines
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Journal ArticleDOI
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.
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Inference from Iterative Simulation Using Multiple Sequences
Andrew Gelman,Donald B. Rubin +1 more
TL;DR: The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.
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Robust Locally Weighted Regression and Smoothing Scatterplots
TL;DR: Robust locally weighted regression as discussed by the authors is a method for smoothing a scatterplot, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i, y i ) is large if x i is close to x k and small if it is not.