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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Volatility, Momentum, and Time-Varying Skewness in Foreign Exchange Returns
TL;DR: In this paper, a stochastic volatility model of exchange rates is proposed that links both the level of volatility and its instantaneous covariance with returns to pathwise properties of the currency.
Posted Content
Extension of Fill's perfect rejection sampling algorithm to general chains
TL;DR: By developing and applying a broad framework for rejection sampling using auxiliary randomness, this work provides an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite general state spaces, and describes how use of bounding processes can ease computational burden.
Journal ArticleDOI
Receiver function deconvolution using transdimensional hierarchical Bayesian inference
TL;DR: In this article, a transdimensional hierarchical Bayesian inference method was proposed to calculate the likelihood probability distribution of a receiver function in which both the noise magnitude and noise spectral character are parameters.
Journal ArticleDOI
Bayesian Elastic Full-Waveform Inversion Using Hamiltonian Monte Carlo
TL;DR: In this article, a proof of concept for Bayesian elastic full-waveform inversion in 2D is presented based on Hamiltonian Monte Carlo sampling of the posterior distribution, and the computation of misfit derivatives using adjoint techniques.
Journal ArticleDOI
Using Bayesian-PBPK modeling for assessment of inter-individual variability and subgroup stratification
Markus Krauss,Rolf Burghaus,Jörg Lippert,Mikko Niemi,Mikko Niemi,Pertti J. Neuvonen,Andreas Schuppert,Andreas Schuppert,Stefan Willmann,Lars Kuepfer,Linus Görlitz +10 more
TL;DR: The presented Bayesian-PBPK approach systematically characterizes inter-individual variability within a population by updating prior knowledge about physiological parameters with new experimental data and allows, in combination with Bayesian approaches, the iterative assessment of specific populations by integrating information from several drugs.
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.