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 approach and extreme value theory in economic analysis of forestry projects
Thiago Taglialegna Salles,Denismar Alves Nogueira,Luiz Alberto Beijo,Liniker Fernandes da Silva +3 more
TL;DR: In this paper, the authors used extreme value theory (EVT) combined with Bayesian inference to predict probability densities for inputs used in economic evaluation criteria like wood yield and prices.
Journal ArticleDOI
Posterior Representations for Bayesian Context Trees: Sampling, Estimation and Convergence
TL;DR: The Bayesian Context Trees (BCT) modelling framework for discrete time series is revisited and a novel representation of the induced posterior distribution on model space is derived in terms of a simple branching process, including the derivation of an almost-sure convergence rate.
Journal ArticleDOI
Parameter estimation of a two-parameter Lindley distribution under hybrid censoring
Bander Al-Zahrani,Maha S Gindwan +1 more
TL;DR: The paper deals with the classical and Bayesian estimation of a two-parameter weighted Lindley distribution based on hybrid censoring and the maximum likelihood estimators with its standard errors are obtained.
Journal ArticleDOI
Difficult risks and capital models
R. Frankland,S. Eshun,L. Hewitt,Parit Jakhria,Stuart Jarvis,A. Rowe,A. D. Smith,A. C. Sharp,James Sharpe,T. Wilkins +9 more
TL;DR: In this paper, the Extreme Events Working Party considered some of the difficulties in calculating capital buffers to cover potential losses and presented a range of tools and techniques to help address some of these difficulties.
References
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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.