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
A Bayesian Monte Carlo Markov Chain Method for Parameter Estimation of Fractional Differenced Gaussian Processes
TL;DR: The results from the simulations suggest that this Bayesian Monte Carlo Markov Chain method is unaffected by the stationary regime and hence, can be used to check whether or not a time series is stationary.
Journal ArticleDOI
Pharmacological interventions for the prevention of acute kidney injury after pediatric cardiac surgery: a network meta-analysis.
TL;DR: It is suggested that no firm evidence exists about the protective role of pharmacological interventions in the pediatric population and future randomized controlled trials should clarify the effectiveness of dexmedetomidine and acetaminophen and indicate the optimal protocol to be applied, to protect renal function in the perioperative setting.
Journal ArticleDOI
Simulation-based bayesian inference using BUGS
Ching-Fan Sheu,Suzanne O'Curry +1 more
TL;DR: This work illustrates the application of BUGS, a Bayesian computer program, with two examples, using a popular Markov chain Monte Carlo procedure called Gibbs sampling.
Journal ArticleDOI
Market Segmentation Using Brand Strategy Research: Bayesian Inference with Respect to Mixtures of Log-Linear Models
TL;DR: A Bayesian modelbased clustering approach for dichotomous item responses that deals with issues often encountered in model based clustering like missing data, large data sets and within cluster dependencies is presented.
Journal ArticleDOI
What do we know about the heritability of developmental instability? answers from a bayesian model
TL;DR: A Bayesian latent variable model is developed and explored and it is shown that with sample sizes currently applied in empirical studies, extremely wide posterior distributions are obtained and data do not allow to distinguish between high and low heritabilities of DI at all.
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
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.