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
Phase randomisation: numerical study of higher cumulants behaviour
TL;DR: In this article, a phase randomisation procedure is reviewed and modified for testing for stationarity in a time series, and applied to a wide range of time series models, including linear stationary, linear non-stationary, non-linear stationary and nonlinear nonstationary processes.
Journal ArticleDOI
Accounting for uncertainty in extremal dependence modeling using Bayesian model averaging techniques
P. Apputhurai,Alec Stephenson +1 more
TL;DR: In this article, the joint tail of an unknown multivariate distribution can be characterized as modeling the tail of each marginal distribution and modeling the dependence structure between the margins, and the authors employ Bayesian model averaging to account for both types of asymptotic behavior.
Posted Content
To What Degree Does Food Assistance Help Poor Households Acquire Enough Food
TL;DR: In this paper, the effects of domestic food assistance (food stamps, WIC, and food pantries) on low-income households in Allegheny County, Pennsylvania were investigated.
Journal ArticleDOI
Two-way Bayesian hierarchical phylogenetic models: An application to the co-evolution of gp120 and gp41 during and after enfuvirtide treatment
Christina M. R. Kitchen,Jing Lu Kroll,Daniel R. Kuritzkes,Erik W. Bloomquist,Steven G. Deeks,Marc A. Suchard +5 more
TL;DR: A two-way-interaction HPM is proposed that provides middle ground between these two extremes and allows us to test for differences in evolutionary pressures across gene regions in multiple patients simultaneously and supports the hypothesis of independence over dependence between the gene regions.
Dissertation
Accelerating Bayesian Inference in Computationally Expensive Computer Models Using Local and Global Approximations
TL;DR: The second part of this thesis introduces a new framework for accelerating MCMC algorithms by constructing local surrogates of the computational model within the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental 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.
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.