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
Bayesian and Frequentist Inference for Ecological Inference: The R×C Case
TL;DR: In this paper, a Bayesian and frequentist approach to ecological inference based on R 3 C contingency tables, including a covariate, is proposed, where the Bayesian model extends the binomial-beta hierarchical model developed by KING, R OSEN and TANNER (1999) from the 2 3 2 case to the R 3C case.
Journal ArticleDOI
Recent development and biomedical applications of probabilistic Boolean networks.
Panuwat Trairatphisan,Andrzej Mizera,Jun Pang,Alexandru-Adrian Tantar,Jochen G. Schneider,Jochen G. Schneider,Thomas Sauter +6 more
TL;DR: A concise yet comprehensive review of the state-of-the-art on PBN modelling is offered in this article, including a comparative discussion on Pbn versus similar models with respect to concepts and biomedical applications.
Journal ArticleDOI
Statistical analyses of population genetic data: new tools, old concepts
François Rousset,Michel Raymond +1 more
TL;DR: Several methods or tests and various software are currently being developed for analyzing data in population genetics and ecology, which often rely on computer-intensive algorithms.
Journal ArticleDOI
Bayesian Smoothing with Gaussian Processes Using Fourier Basis Functions in the spectralGP Package
TL;DR: The spectral representation of stationary Gaussian processes via the Fourier basis provides a computationally efficient specification of spatial surfaces and nonparametric regression functions for use in various statistical models.
Journal ArticleDOI
Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis.
TL;DR: This work presents a novel method for fitting the full Bayesian model in two stages, hence benefiting from its advantages while retaining the convenience and flexibility of a two-stage approach.
References
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Equation of state calculations by fast computing machines
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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
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Monte Carlo Sampling Methods Using Markov Chains and Their Applications
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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.
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.