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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Modeling collision probability for Earth-impactor 2008 TC3
Dagmara Oszkiewicz,Karri Muinonen,Karri Muinonen,Jenni Virtanen,Mikael Granvik,Edward Bowell +5 more
TL;DR: In this paper, the authors study the evolution of the Earth collision probability of asteroid 2008 TC 3 using a short observational arc and small numbers of observations, using techniques that rely on the orbital-element probability density function characterized using both Markov-chain Monte-Carlo orbital ranging and Monte Carlo ranging.
Journal ArticleDOI
Multivariate regression analysis of panel data with binary outcomes applied to unemployment data
TL;DR: In this article, Czado et al. developed a Markov Chain Monte Carlo (MCMC) algorithm to overcome the difficulty of a likelihood analysis of the multivariate probit model with general correlation structure for higher dimensions.
Journal ArticleDOI
Advances on methods for mapping QTL in plant
TL;DR: The purpose is to direct plant geneticists to choose a suitable method in the inheritance analysis of quantitative trait and in search of novel genes in germplasm resource so that more potential genetic information can be uncovered.
Journal ArticleDOI
Model predictive control with active learning for stochastic systems with structural model uncertainty: Online model discrimination
TL;DR: This paper addresses control of stochastic nonlinear systems using model predictive control, or mpc, under structural model uncertainty with a strategy with active learning that can probe the uncertain system to select the model that best describes the observed closed-loop system data.
Journal ArticleDOI
Affective parameter shaping in user experience prospect evaluation based on hierarchical Bayesian estimation
TL;DR: The cumulative prospect theory quantitatively fulfills user experience evaluation by developing a hierarchical Bayesian model via Markov chain Monte Carlo technique for parameter estimation under three affective states and demonstrating the proposed method via a aircraft cabin interior design.
References
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Journal ArticleDOI
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.