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
Extinction under a Behavioral Microscope: Isolating the Sources of Decline in Operant Response Rate
TL;DR: The authors proposed an analytic procedure that separates extinction performance into several behavioral components: (1) the baseline bout initiation rate, within-bout response rate, and bout length at the onset of extinction; (2) their rates of decay during extinction, (3) the time between extinction onset and the decline of responding; (4) the asymptotic response rate at the end of extinction.
Journal ArticleDOI
Bayesian geological and geophysical data fusion for the construction and uncertainty quantification of 3D geological models
Hugo K.H. Olierook,Richard Scalzo,David Kohn,Rohitash Chandra,Rohitash Chandra,Ehsan Farahbakhsh,Chris D. Clark,Steven M. Reddy,R. Dietmar Müller +8 more
TL;DR: In this article, the Bayesian Obsidian software package is used to fuse lithostratigraphic field observations with aeromagnetic and gravity data to build a 3D model in a small region of the Gascoyne Province, Western Australia.
Book Chapter
Notes on perfect simulation
TL;DR: Five expository essays by leaders in the field of Markov Chain Monte Carlo are presented, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts.
Journal ArticleDOI
Dynamic Discrete-time Duration Models: Estimation via Markov Chain Monte Carlo
TL;DR: Dynamic models for flexible Bayesian nonparametric analysis of unemployment duration data allow simultaneous incorporation and estimation of baseline hazards and time-varying covariate effects, with out imposing particular parametric forms.
Journal ArticleDOI
Arbitrary Importance Functions for Metropolis Light Transport
Jared Hoberock,John Hart +1 more
TL;DR: This work introduces alternative importance functions, which encourage the Markov chain to aggressively pursue sampling goals of interest to the user and proves that these importance functions may adapt over the course of a render in an unbiased fashion.
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.