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
Quantile regression for longitudinal data using the asymmetric Laplace distribution
Marco Geraci,Matteo Bottai +1 more
TL;DR: A novel linear model for quantile regression (QR) that includes random effects in order to account for the dependence between serial observations on the same subject is proposed and appears to be a robust alternative to the mean regression with random effects when the location parameter of the conditional distribution of the response is of interest.
Journal ArticleDOI
Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem
TL;DR: In this paper, a Markov chain Monte Carlo (MCMC) algorithm is applied to the nonlinear problem of inverting DC resistivity sounding data to infer characteristics of a 1-D earth model.
Journal ArticleDOI
Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography
TL;DR: In this paper, the authors consider the electrical impedance tomography (EIT) problem in the framework of Bayesian statistics, where the inverse problem is recast into a form of statistical inference.
Journal ArticleDOI
The Variable Selection Problem
TL;DR: This vignette reviews some of the key developments that have led to the wide variety of approaches for the problem of subset selection in statistical applications.
Posted Content
The Signaling Channel for Federal Reserve Bond Purchases
TL;DR: In this article, a model-free analysis and dynamic term structure models were used to decompose declines in yields following Fed announcements into changes in risk premia and expected short rates.
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.