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
The influence of spatio-temporal resource fluctuations on insular rat population dynamics
James C. Russell,Lise Ruffino +1 more
TL;DR: Surprisingly for a generalist forager, movement between habitats was rare, suggesting individuals do not opportunistically respond to spatial resource subsidy variations, and Marked variation in survival and capture has important implications for the timing of rat control.
Journal ArticleDOI
Bayesian statistical method was underused despite its advantages in the assessment of implantable medical devices
TL;DR: The underuse of Bayesian methods in IMD assessment was highlighted, and the major challenge is to provide to clinical researchers a framework that helps them use external evidence to elicit prior distributions.
Journal ArticleDOI
A Functional Time Warping Approach to Modeling and Monitoring Truncated Degradation Signals
TL;DR: A flexible modeling framework for characterizing degradation signals that can only be observed up to a prespecified failure threshold is presented and real-time predictions for the residual lifetime of components deployed in the field are obtained.
Journal ArticleDOI
Bayesian Inference for Functional Response in a Stochastic Predator–Prey System
TL;DR: A Bayesian method for functional response parameter estimation starting from time series of field data on predator–prey dynamics, which considers an acarine predator-prey system relevant to biological control problems.
Journal ArticleDOI
Sequential, Bayesian Geostatistics: A Principled Method for Large Data Sets
TL;DR: This article presents a Bayesian method for estimating the posterior mean and covariance structures of a Gaussian random field using a sequential estimation algorithm that retains a subset of “basis vectors” that best represent the “true” posterior Gaussianrandom field model in the relative entropy sense.
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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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
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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.