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
Harvest-based Bayesian estimation of sika deer populations using state-space models
Kohji Yamamura,Hiroyuki Matsuda,Hiroyuki Yokomizo,Hiroyuki Yokomizo,Koichi Kaji,Hiroyuki Uno,Katsumi Tamada,Toshio Kurumada,Takashi Saitoh,Hirofumi Hirakawa +9 more
TL;DR: It is able to demonstrate that the harvest-based Bayesian estimation is effective in reducing the observation errors in sika deer populations, but the stage-structured model requires many demographic parameters to be known prior to running the analyses.
Journal ArticleDOI
A Bayesian approach to estimate the marginal loss distributions in operational risk management
L. Dalla Valle,Paolo Giudici +1 more
TL;DR: An original proposal is a Bayesian approach for modelling operational risk and for calculating the capital required to cover the estimated risks, based on Markov chain Monte Carlo simulations, which shows advantages in terms of a reduction of capital charge according to different choices of the marginal loss distributions.
Journal ArticleDOI
Monochloramine Disinfection Kinetics of Nitrosomonas europaea by Propidium Monoazide Quantitative PCR and Live/Dead BacLight Methods
TL;DR: This is the first published application of a PMA-qPCR method for disinfection kinetic model parameter estimation as well as its application to N. europaea or monochloramine, the lag phase was not previously reported for culture-independent methods and may have implications for nitrification in drinking water distribution systems.
Journal ArticleDOI
A robust-design formulation of the incidence function model of metapopulation dynamics applied to two species of rails.
TL;DR: It is suggested that incorporating false absences and missing data into the IFM can improve estimates of dispersal ability and the effect of connectivity on colonization, the scaling of extinction risk with patch area, and forecasts of occupancy and turnover rates.
Journal ArticleDOI
Mapping multiple Quantitative Trait Loci by Bayesian classification.
TL;DR: A classification approach to multiple quantitative trait loci (QTL) mapping built upon a Bayesian framework that incorporates the important prior information that most genotypic markers are not cotransmitted with a QTL or their QTL effects are negligible is developed.
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.
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.
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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.