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
Distribution Transformer's Loss of Life Considering Residential Prosumers Owning Solar Shingles, High-Power Fast Chargers and Second-Generation Battery Energy Storage
TL;DR: The effectiveness of the second-generation residential home and community battery energy storage, installed in the residential prosumers and in the electric utilities’ premises, in preserving the distribution transformer's lifetime is discussed and conclusions are drawn.
Journal ArticleDOI
Bayesian Modeling of Markers of Day-Specific Fertility
David B. Dunson,Bernardo Colombo +1 more
TL;DR: A Bayesian approach for modeling of daily observations of cervical mucus is developed and the approach to assess heterogeneity among women and cycles from a given woman with respect to the increase in mucus hydration during the fertile interval is applied.
Journal ArticleDOI
Estimation Using Censored Data from Exponentiated Burr Type XII Population
TL;DR: In this article, maximum likelihood and Bayes estimators of the parameters, survival function (SF) and hazard rate function (HRF) are obtained for the three-parameter exponentiated Burr type XII distribution when sample is available from type II censored scheme.
Journal ArticleDOI
A Bayesian analysis of a variance decomposition for stock returns
TL;DR: In this article, the authors apply Bayesian methods to study a common vector autoregression (VAR)-based approach for decomposing the variance of excess stock returns into components reflecting news about future excess stock return, future real interest rates, and future dividends.
Journal ArticleDOI
Asymmetric impact of renewable and non-renewable energy on the industrial sector in Pakistan: Fresh evidence from Bayesian and non-linear ARDL
TL;DR: In this article , the authors investigated the asymmetric relationship between renewable energy consumption (REC), non-renewable energy (NRE), terrorism, inflation, and international trade in the industrial sector from 1970 to 2018 in Pakistan.
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.
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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.