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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Proceedings ArticleDOI
Bayesian integration of biological prior knowledge into the reconstruction of gene regulatory networks with Bayesian networks.
TL;DR: This work has derived and tested an MCMC scheme for sampling networks and hyperparameters simultaneously from the posterior distribution and assessed the viability of this approach by reconstructing the RAF pathway from cytometry protein concentrations and prior knowledge from KEGG.
Essays on Neural Network Sampling Methods and Instrumental Variables
TL;DR: Hoogerheide et al. as discussed by the authors present a nieuwe, op neurale netwerken gebaseerde, methode with verschillende bekende methoden, which blijkt betrouwbaar en snel te zijn.
Journal ArticleDOI
Bayesian Kriging Analysis and Design for Stochastic Simulations
Szu Hui Ng,Jun Yin +1 more
TL;DR: A Bayesian metamodeling approach for kriging prediction is proposed for stochastic simulations to more appropriately account for the parameter uncertainties and a two-stage design approach is proposed that systematically balances the allocation of computing resources to new design points and replication numbers in order to reduce the uncertainties and improve the accuracy of the predictions.
Journal Article
Estimating ratios of normalizing constants for densities with different dimensions
Ming-Hui Chen,Qi-Man Shao +1 more
TL;DR: In this paper, the authors extend importance sampling, bridge sampling, and ratio importance sampling to problems of different dimensions and find global optimal importance sampling and bridge sampling in the sense of minimizing asymptotic relative mean-square errors of estimators.
Journal ArticleDOI
Improving Efficiency of the Bayesian Approach to Water Distribution Contaminant Source Characterization with Support Vector Regression
Hui Wang,Kenneth W. Harrison +1 more
TL;DR: In this article, Markov chain Monte Carlo (MCMCMC) methods for Bayesian analyses allow for the characterization of the uncertainty in the contamination event profile, which has been shown in some circumstances to be necessary if the contaminant event is to be properly characterized.
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.
Journal ArticleDOI
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.
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.