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
Bayesian Analysis of Realistically Complex Models
TL;DR: Models with complex structure arise in many social science applications and appear natural candidates for the use of Markov chain Monte Carlo methods for inference, including random effects models for repeated ordered categorical data and sensitivity analysis to assumptions concerning the mechanism underlying informative drop‐out in a longitudinal study.
Journal ArticleDOI
On Marker-Assisted Prediction of Genetic Value: Beyond the Ridge
TL;DR: Here, phenotype-marker associations are modeled hierarchically via multilevel models including chromosomal effects, a spatial covariance of marked effects within chromosomes, background genetic variability, and family heterogeneity, and Bayesian methods are presented.
Journal ArticleDOI
Global model analysis by parameter space partitioning.
TL;DR: Parameter space partitioning is a solution that evaluates model performance at a qualitative level and three application examples demonstrate its potential and versatility for studying the global behavior of psychological models.
Journal ArticleDOI
Parameter uncertainty in biochemical models described by ordinary differential equations.
J Joep Vanlier,J Joep Vanlier,CA Christian Tiemann,CA Christian Tiemann,Peter A. J. Hilbers,Peter A. J. Hilbers,N.A.W. van Riel,N.A.W. van Riel +7 more
TL;DR: This review provides an introduction to some of the techniques available as well as gives an overview of the state-of-the-art methods for parameter uncertainty analysis.
Journal ArticleDOI
Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy
TL;DR: The basics of Bayesian theory are explained and how to set up data analysis problems within this framework are discussed, and an overview of various Monte Carlo based methods for performing Bayesian data analysis is provided.
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.
Journal ArticleDOI
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.