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
Inference in randomized trials with death and missingness.
TL;DR: A procedure for comparing treatments that is based on a composite endpoint that combines information on both the functional outcome and survival and a missing data imputation scheme and sensitivity analysis strategy to handle the unobserved functional outcomes not due to death are proposed.
Journal ArticleDOI
Survival and spatial fidelity of mouflons: The effect of location, age, and sex
Ruth King,Stephen Brooks +1 more
TL;DR: It is shown that survival rates tend to remain constant with some evidence to suggest a slight senescent decline, and evidence is provided to suggest that movement around the habitat is largely the same for both sexes up until age 4, when the males appear to extend their migration range, venturing further from the main flock in search of better grazing.
Posted Content
Relative fixed-width stopping rules for Markov chain Monte Carlo simulations
James M. Flegal,Lei Gong +1 more
TL;DR: In this paper, the authors propose relative magnitude and relative standard deviation stopping rules in the context of Markov chain Monte Carlo (MCMC) simulations for estimating features of a target distribution, particularly for Bayesian inference.
Journal ArticleDOI
Employment Insecurity, Incumbent Partisanship, and Voting Behavior in Comparative Perspective:
TL;DR: The authors argue that occupational unemployment rates, by informing perceptions of economic insecurity, serve as a salient and powerful heuristic for aggregate economic performance, and that high and low unemployment rates serve as heuristics for economic performance.
Journal ArticleDOI
Evolution of Human Immunodeficiency Virus Type 1 Coreceptor Usage during Antiretroviral Therapy: a Bayesian Approach
Christina M. R. Kitchen,Sean Philpott,Harold Burger,Barbara Weiser,Kathryn Anastos,Marc A. Suchard +5 more
TL;DR: A Bayesian hierarchical model is developed that incorporates all available sequence data while simultaneously allowing the phylogenetic parameters of each patient to vary to examine evolutionary changes in HIV-1 coreceptor usage in response to treatment and found that the reemergent R5 virus detectable after therapy was more closely related to the predecessor R5irus than to the X4 strains.
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.
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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.