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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MultiBUGS: A parallel implementation of the BUGS modelling framework for faster Bayesian inference
TL;DR: A new version of the general-purpose Bayesian modelling software BUGS that implements a generic algorithm for parallelising Markov chain Monte Carlo algorithms to speed up posterior inference of Bayesian models, making the dramatic speed-ups of modern multi-core computing accessible to applied statisticians, without requiring any experience of parallel programming.
Dissertation
Social and Spatial Determinants of Adverse Birth Outcome Inequalities in Socially Advanced Societies
Journal ArticleDOI
Efficient direct sampling MCEM algorithm for latent variable models with binary responses
Xinming An,Peter M. Bentler +1 more
TL;DR: Results from two simulation studies and a real data example suggest that, as compared with MCMC based EM, DSMCEM can significantly improve computational efficiency as well as produce equally accurate parameter estimates.
Journal ArticleDOI
Dark-age reionization and galaxy formation simulation – XIX. Predictions of infrared excess and cosmic star formation rate density from UV observations
TL;DR: In this paper, the authors present a new analysis of high-redshift UV observations using a semi-analytic galaxy formation model, and provide self-consistent predictions of the infrared excess (IRX)-β relations and cosmic star formation rate density.
Possibly Ill-behaved Posteriors in Econometric Models: On the Connection between Model Structures, Non-elliptical Credible Sets and Neural Network Simulation Techniques
TL;DR: In this article, the authors consider the possibility of highly non-elliptical posterior distributions that may occur in several econometric models, in particular, when the information in the data is weak.
References
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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.
Journal ArticleDOI
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
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Journal ArticleDOI
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.
Journal ArticleDOI
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.