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
Cluster modelling of disease incidence via RJMCMC methods: a comparative evaluation
TL;DR: Individual frailty is also considered important and a computational algorithm based on reversible jump Markov chain Monte Carlo (RJMCMC) methods is described, which addresses the need for specific and non-specific random effects within spatial epidemiology.
Proceedings ArticleDOI
Probabilistic Verification of Network Configurations
TL;DR: NetDice is introduced, the first scalable and accurate probabilistic network configuration analyzer supporting BGP, OSPF, ECMP, and static routes and automatically identifies a set of links whose failure is provably guaranteed not to change whether φ holds.
Book ChapterDOI
Detecting Lateral Genetic Transfer
Robert G. Beiko,Mark A. Ragan +1 more
TL;DR: This chapter outlines how bioinformatic and phylogenetic analyses can be built into a workflow to identify LGT among microbial genomes.
Journal ArticleDOI
Short-range order in face-centered cubic VCoNi alloys
Tatiana Kostiuchenko,Andrei V. Ruban,Jörg Neugebauer,Alexander V. Shapeev,Fritz Körmann,Fritz Körmann +5 more
TL;DR: In this article, the degree of potential short-range order (SRO) for VCoNi was computed by utilizing the coherent-potential approximation in combination with the generalized perturbation method as well as the supercell method in addition with recently developed machine-learned potentials.
Approximate inference for robust Gaussian process regression
TL;DR: A case study is presented describing its implementation for a new robust variant of Gaussian process regression and experiments are presented in which results obtained by Markov chain Monte Carlo (MCMC) sampling are compared to results obtained from expectation-propagation.
References
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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
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Journal ArticleDOI
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.
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.