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 two-step method for detecting selection signatures using genetic markers
TL;DR: A two-step procedure is presented for analysis of θ (FST) statistics obtained for a battery of loci, which eventually leads to a clustered structure of values, which would reflect different types of processes and would assist in interpreting results.
Journal ArticleDOI
Bayesian cure rate frailty models with application to a root canal therapy study.
TL;DR: This work proposes two forms of cure rate frailty models, one of which naturally introduces frailty based on biological considerations while the other is motivated from the Cox proportional hazards frailty model.
Journal ArticleDOI
On estimation and influence diagnostics for log-Birnbaum–Saunders Student-t regression models: Full Bayesian analysis
TL;DR: In this paper, a Bayesian approach for log-Birnbaum-Saunders Student-t regression models under right-censored survival data is developed, where Markov chain Monte Carlo (MCMCMC) methods are used to develop a bayesian procedure for the considered model.
Book ChapterDOI
Sampling connected induced subgraphs uniformly at random
Xuesong Lu,Stéphane Bressan +1 more
TL;DR: This paper devise, present and discuss several algorithms that leverage three different techniques: Rejection Sampling, Random Walk and Markov Chain Monte Carlo, and proposes one novel algorithm, which is called Neighbour Reservoir Sampling (NRS), that very successfully realizes the trade-off between effectiveness and efficiency.
Journal ArticleDOI
Markov chain monte carlo methods for switching diffusion models
John Liechty,Gareth O. Roberts +1 more
TL;DR: In this paper, Markov chain Monte Carlo (MCMCMC) was used to analyse continuous-time latent models, sometimes known as state space models or hidden Markov models.
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.