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
Difficulties in the use of auxiliary variables in Markov chain Monte Carlo methods
TL;DR: The results suggest that adapting the auxiliary variables to the specific application is beneficial, however the form of adaptation needed and the extent of the resulting benefits are not always clear-cut.
Journal ArticleDOI
Regional variability in diving physiology and behavior in a widely distributed air-breathing marine predator, the South American sea lion (Otaria byronia)
Luis A. Hückstädt,Michael S. Tift,Federico G. Riet-Sapriza,Valentina Franco-Trecu,Alastair M. M. Baylis,Rachael A. Orben,John P. Y. Arnould,Maritza Sepúlveda,Macarena Santos-Carvallo,Jennifer M. Burns,Daniel P. Costa +10 more
TL;DR: The study suggests that the physiology of air-breathing diving predators is not fixed, but that it can be adjusted, to a certain extent, depending on the ecological setting and or habitat.
Journal ArticleDOI
A stochastic rank ordered logit model for rating multi-competitor games and sports
TL;DR: A Bayesian state-space framework for rank ordered logit models to rate competitor abilities over time from the results of multi-competitor games is proposed and a filtering algorithm is developed that is an approximation to the full Bayesian computations.
Journal ArticleDOI
Spatial competing risk models in disease mapping.
TL;DR: This work examines the use of weighting schemes within the general formulation, and extensions to count data and spatio-temporal modelling, which leads to the consideration of the joint spatial distribution of a 'basket' of diseases.
Journal ArticleDOI
Fast Maximum Likelihood Estimation via Equilibrium Expectation for Large Network Data.
Maksym Byshkin,Alex Stivala,Alex Stivala,Antonietta Mira,Garry Robins,Garry Robins,Alessandro Lomi,Alessandro Lomi +7 more
TL;DR: In this paper, the authors propose a fast algorithm for maximum likelihood estimation (MLE) that affords a significant increase in the size of networks amenable to direct empirical analysis.
References
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Equation of state calculations by fast computing machines
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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
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.