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
Teaching Bayesian Statistics in a Health Research Methodology Program
TL;DR: Teaching a course in Bayesian methods to a group of health research methodologists can be challenging because most statisticians have been taughtBayesian methods using a mathematical approach, and this must be adapted in order to communicate with non-statisticians.
Journal ArticleDOI
Improved Tabu Search and Simulated Annealing methods for nonlinear data assimilation
Elias D. Nino-Ruiz,Xin-She Yang +1 more
TL;DR: Four local search methods for nonlinear data assimilation can converge faster to posterior modes when sub-space approximations are employed to reduce the computational efforts among iterations.
Journal ArticleDOI
An integrated Markov chain Monte Carlo algorithm for upscaling hydrological and geochemical parameters from column to field scale.
TL;DR: The results from MCMC analysis indicated that geochemical upscaling coefficients based on effective concentration ratios incorporating local heterogeneity across layered and lensed systems produced better estimates of redox-sensitive biogeochemistry at the field scale, and inclusion of hydrological parameters in theUpscaling scheme reduced the output uncertainty of effective mean geochemical concentrations by orders of magnitude at the Norman Landfill site.
Journal ArticleDOI
Different Surgical Strategies in the Prevention of Frey Syndrome: A Systematic Review and Meta-analysis.
Armando De Virgilio,Andrea Costantino,Elena Russo,Fabio Ferreli,Raul Pellini,Gerardo Petruzzi,Jacopo Zocchi,Giuseppe Spriano,Giuseppe Mercante +8 more
TL;DR: In this paper, an arm-based network analysis was conducted using a Bayesian hierarchical model to define the best surgical technique able to reduce Frey syndrome (FS) incidence after parotidectomy.
Journal ArticleDOI
Forecasting Stock Prices Using a Hierarchical Bayesian Approach
Jun Ying,Lynn Kuo,Gim S. Seow +2 more
TL;DR: In this paper, a hierarchical Bayesian approach is developed to simultaneously estimate the unknown coefficients in the time series regression model for each company by pooling information across firms, and the prediction is carried out by the Markov chain Monte Carlo (MCMC) method.
References
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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.
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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.
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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.