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
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Book
Bayesian Econometric Methods
TL;DR: This volume in the Econometric Exercises series contains questions and answers to provide students with useful practice, as they attempt to master Bayesian econometrics.
Journal ArticleDOI
Missing covariates in generalized linear models when the missing data mechanism is non-ignorable
TL;DR: A method for estimating parameters in generalized linear models with missing covariates and a non‐ignorable missing data mechanism and sensitivity analyses play an important role in this problem are discussed in detail.
Journal ArticleDOI
Statistical Interpretation of Species Composition
TL;DR: In this article, a hierarchical statistical model that combines Aitchison's logistic normal distribution with a conditional multinomial observation distribution was developed to evaluate the relationship between omnivorous feeding linkages and community stability.
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Reconstructing Gene Regulatory Networks with Bayesian Networks by Combining Expression Data with Multiple Sources of Prior Knowledge
TL;DR: These findings quantify to what extent the inclusion of independent prior knowledge improves the network reconstruction accuracy, and the values of the hyperparameters inferred with the proposed scheme were found to be close to optimal with respect to minimizing the reconstruction error.
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A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing
TL;DR: In this paper, a Bayesian variable-selection algorithm based on a variable selection algorithm is proposed for searching the model space more thoroughly. But the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models.
References
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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.
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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.
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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.
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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.