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 approach to investigate life course hypotheses involving continuous exposures.
Sreenath Arekunnath Madathil,Lawrence Joseph,Rebecca Hardy,Marie-Claude Rousseau,Marie-Claude Rousseau,Belinda Nicolau +5 more
TL;DR: This work proposes an alternative technique for a continuous exposure, using a Bayesian approach that has specific advantages, to investigate which life course hypotheses are supported by the observed data, and demonstrates the technique, the relevant life course exposure model (RLM), using simulations.
Journal ArticleDOI
Testing the efficiency of Markov Chain Monte Carlo with people using facial affect categories
TL;DR: This work applies Markov chain Monte Carlo with People (MCMCP) and reverse correlation to the problem of recovering natural categories that correspond to two kinds of facial affect from realistic images of faces, and shows that MCMCP requires fewer trials to obtain a higher quality estimate of people's mental representations of these two categories.
Journal ArticleDOI
Bayesian variable selection for the Cox regression model with missing covariates.
TL;DR: A new joint semi-conjugate prior for the piecewise exponential model is proposed in the presence of missing covariates and a version of the Deviance Information Criterion (DIC) is proposed for Bayesian variable subset selection for Cox proportional hazards models with missing covariate data.
Journal ArticleDOI
NASA Uncertainty Quantification Challenge: An Optimization-Based Methodology and Validation
TL;DR: A novel cumulative density function matching method is proposed, which gave similar results as a standard Markov chain–Monte Carlo-based Bayesian approach in uncertainty characterization, sensitivity analysis, uncertainty propagation, and extreme-case analysis.
Journal ArticleDOI
Incorporating temporal variation in the growth of red abalone (Haliotis rufescens) using hierarchical Bayesian growth models
Yan JiaoY. Jiao,Laura Rogers-BennettL. Rogers-Bennett,Ian TaniguchiI. Taniguchi,John ButlerJ. Butler,Paul CroneP. Crone +4 more
TL;DR: Bayesian hierarchical models were developed to describe variability in growth rates for the Johnsons Lee red abalone population and suggest that the Bayesian hierarchical modeling estimates are close to estimates of the nonhierarchical highly parameterized model.
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
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.
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.