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
Reliable and fast estimation of recombination rates by convergence diagnosis and parallel Markov Chain Monte Carlo
TL;DR: An improved algorithm based on LDhat implementing MCMC convergence diagnostic algorithms to automatically predict values of parameters and monitor the mixing process is designed, proving that they are more efficient and reliable for the estimation of recombination rates.
Journal ArticleDOI
A Bayesian dose-response meta-analysis model: A simulations study and application
TL;DR: In this paper, a hierarchical dose-response model implemented in a Bayesian framework is proposed to allow maximum flexibility, the doseresponse association is modelled using restricted cubic splines, and they compare their approach to the one-stage doseresponse meta-analysis model in a simulation study.
On the robustness of optimal scaling for random walk metropolis algorithms
TL;DR: In this article, the authors considered the optimal scaling problem for sampling from a target distribution of interest using a random walk Metropolis (RWM) algorithm. And they proposed a method to determine the optimal form for the proposal scaling as a function of d. They also showed that inhomogeneous proposal distributions are sometimes essential to obtain a nontrivial limit.
Journal ArticleDOI
A bayesian perspective on estimation of variability and uncertainty in mechanism-based models.
TL;DR: A perspective on the utility of Markov chain Monte Carlo Bayesian estimation for incorporation of prior information into mechanism‐based models for hypothesis generation and extrapolation beyond the conditions of the original analysis data is provided.
Journal ArticleDOI
Prehospital point of care testing for the early detection of shock and prediction of lifesaving interventions
Samuel M. Galvagno,Robert Sikorski,Douglas J. Floccare,Peter Rock,Michael A. Mazzeffi,Joseph J. DuBose,Thomas M. Scalea,Catriona Miller,Justin E. Richards,James V. O’Connor,Colin F. Mackenzie,Peter Hu +11 more
TL;DR: Lactate outperformed static vital signs, including shock index, for detecting shock and predicting the need for LSIs in adult patients with traumatic injuries in a prospective prehospital observational study.
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.
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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.
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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.