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 latent Gaussian model for compositional data with zeros
Adam Butler,Chris A. Glasbey +1 more
TL;DR: A latent Gaussian model for the analysis of compositional data which contain zero values is presented, based on assuming that the data arise from a (deterministic) Euclidean projection of a multivariate Gaussian random variable onto the unit simplex.
Journal ArticleDOI
Using Pathway-Specific Comprehensive Exposure Scores in Epidemiology: Application to Oxidative Balance in a Pooled Case-Control Study of Incident, Sporadic Colorectal Adenomas
Chiranjeev Dash,Michael Goodman,W. Dana Flanders,Pamela J. Mink,Marjorie L. McCullough,Roberd M. Bostick +5 more
TL;DR: Findings suggest that OBS are indicators of oxidative balance and may be inversely associated with colorectal adenoma risk and using comprehensive exposure scores may be preferable to investigating individual component-disease associations for complex exposures, such as oxidative balance.
Journal ArticleDOI
Regional flood frequency analyses involving extraordinary flood events at ungauged sites: further developments and validations
TL;DR: In this article, a combination of the two techniques aiming at including estimated extreme discharges at ungauged sites of a region in the regional flood frequency analyses has been proposed.
Journal ArticleDOI
Modelling multi-hazard threats to cultural heritage sites and environmental sustainability: The present and future scenarios
Asish Saha,Subodh Chandra Pal,M. Santosh,M. Santosh,Saeid Janizadeh,Indrajit Chowdhuri,Akbar Norouzi,Paramita Roy,Rabin Chakrabortty +8 more
TL;DR: In this paper, a multi-hazard susceptibility mapping and evaluation of its risk assessment in some of the famous cultural heritage sites in the eastern Himalayan region of Sikkim state, India was performed using boosted regression tree (BRT), Bayesian additive regression trees (BART), and Bayesian generalized linear model (BGLM) considering twenty-two conditioning factors and seismic activity, as this region is highly susceptible to earthquakes.
Book ChapterDOI
An Introduction to MCMC
TL;DR: Markov chain Monte Carlo algorithms are now widely used in virtually all areas of statistics, but spatial applications featured very prominently in the early development of the methodology, and they still provide some of the most challenging problems for MCMC techniques.
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.
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.