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 mixed‐effect model for positive responses augmented by zeros
Mariana Rodrigues-Motta,Diana Milena Galvis Soto,Victor H. Lachos,Filidor Vilca,Valéria Troncoso Baltar,Eliseu Verly Junior,Regina Mara Fisberg,Dirce Maria Lobo Marchioni +7 more
TL;DR: This research article proposes a class of models for positive and zero responses by means of a zero-augmented mixed regression model and applies the proposed method to a dataset from a 24 hour dietary recall study conducted in the city of São Paulo.
Journal ArticleDOI
Use of Bayesian Markov chain Monte Carlo methods to estimate EQ-5D utility scores from EORTC QLQ data in myeloma for use in cost-effectiveness analysis
Samer A. Kharroubi,Richard Edlin,David Meads,Chantelle Browne,Julia Brown,Christopher McCabe +5 more
TL;DR: The relative advantage of the Bayesian methods in relation to dealing with missing data is examined, relaxing the assumption of equal variances and characterizing the uncertainty in the model predictions, to help inform analyses for probabilistic CEAs.
A model of the product lifecycle for sales forecasting
TL;DR: In this paper, the authors describe a forecasting system at Sun Microsystems, Inc. (a major manufacturer of network computer products) that combines a diffusion model to describe transitional sales with very general constructs for time series analysis known as dynamic linear models (DLMs).
Dissertation
Bayesian inference for protein signalling networks
TL;DR: This thesis sought to develop novel statistical methods on the problems of elucidating biochemical network topology from assay data and prediction of dynamical response to therapy when both network and parameters are uncertain.
Journal ArticleDOI
Marginal Likelihood for a Class of Bayesian Generalized Linear Models
Balgobin Nandram,Hyunjoong Kim +1 more
TL;DR: The marginal likelihood for a class of generalized linear models used in small area estimation for mortality data analysis, and a simulation study in which the marginal likelihood is used to investigate the improvement in the goodness of fit of one hierarchical Poisson regression model over the other.
References
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Equation of state calculations by fast computing machines
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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
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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.