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 inference for smooth transition autoregressive (STAR) model: A prior sensitivity analysis
Glen Livingston,Darfiana Nur +1 more
TL;DR: The joint posterior distribution of model order, coefficient, and implicit parameters in the logistic STAR model is presented, and the conditional posterior distributions are shown, followed by the design of a posterior simulator using a combination of Metropolis-Hastings, Gibbs Sampler, RJMCMC, and Multiple Try Metropolis algorithms.
Journal ArticleDOI
Bayesian modeling and optimization for multi-response surfaces
TL;DR: It is shown that the Bayesian SUR models can provide more flexible and accurate modeling than the standard multivariate regression (SMR) models with the same covariate structure across different responses.
Journal ArticleDOI
Selection for increased body length in Subantarctic fur seals on Amsterdam Island.
TL;DR: Using a Bayesian multi‐trait ‘animal model’, the quantitative genetics of body size, a fitness‐related trait, in Subantarctic fur seals (Arctocephalus tropicalis) breeding on Amsterdam Island, Southern Ocean is investigated.
Journal ArticleDOI
Bayesian Accelerated Life Testing under Competing Weibull Causes of Failure
TL;DR: In this paper, a general stress translation function of location parameter of the component log-lifetime distribution is proposed which can accommodate standard ones like Arrhenius, power-rule, loglinear model, etc., as special cases.
Proceedings ArticleDOI
Predictability and Prediction of Human Mobility Based on Application-Collected Location Data
TL;DR: This paper implements a clustering method based on the contextual information that cluster the locations into three divisions, street, district and region and employs a high-order Markov chain model to predict the most likely locations visited by each user.
References
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Equation of state calculations by fast computing machines
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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
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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.