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
A smoothing algorithm for estimating stochastic, continuous time model parameters and its application to a simple climate model
TL;DR: A Markov chain Monte Carlo algorithm for Bayesian estimation of parameters jointly with the other, constant, parameters of the model and demonstrates the technical feasibility of the smoothing technique but also the need for a careful interpretation of the results.
Journal ArticleDOI
Bayesian Hierarchical Poisson Regression Models: An Application to a Driving Study with Kinematic Events
TL;DR: It is shown that driving with a passenger and night driving decrease kinematic events, while having risky friends increases these events, which will be useful for other intensively collected longitudinal count data, where event rates are low and interest focuses on estimating the mean and variance structure of the process.
Journal ArticleDOI
Term Premia and the News
TL;DR: In this article, a dynamic term structure model (DTSM) is proposed to estimate monetary policy expectations and term premia in response to macroeconomic news, which leads to more precise and more reliable estimates of expectation and term premium components.
OtherDOI
Markov Chain Monte Carlo Methods
TL;DR: Although the purpose of this book is to introduce some control techniques for such simulation methods, it is necessary to recall in this chapter the main properties of Markov Chain Monte Carlo (MCMC) algorithms.
Journal ArticleDOI
Stochastic volatility: Bayesian computation using automatic differentiation and the extended Kalman filter
TL;DR: An efficient MCMC algorithm for posterior computation in SV models is presented and is compared to the single-update Gibbs sampler and the integration sampler using a well-known time series of pound/dollar exchange rates.
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.