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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Parameter Estimation of Marshall-Olkin Extended Exponential distribution using Markov Chain Monte Carlo Method for Informative set of priors
TL;DR: In this paper, the authors used the Markov Chain Monte Carlo (MCMC) method to compute the Bayes estimates of the model parameters and also assumed that the parameters have informative set of priors and they are independently distributed.
Dissertation
Bayesian models for longitudinal data
TL;DR: In this paper, the authors developed Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited, and applied these models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland.
Journal ArticleDOI
Sensitivity Analysis Using Elicited Expert Information for Inference With Coarsened Data: Illustration of Censored Discrete Event Times in the AIDS Link to Intravenous Experience (ALIVE) Study
TL;DR: A sensitivity analysis is performed using information elicited from 2 ALIVE scientists and an expert in acquired immunodeficiency syndrome epidemiology about the relation between seroconversion and censoring to compare cumulative incidence functions of censored nonmortality outcomes.
DissertationDOI
Generalised Bayesian Matrix Factorisation Models
TL;DR: This paper aims to demonstrate the efforts towards in-situ applicability of EMMARM, as to provide real-time information about concrete mechanical properties such as E-modulus and compressive strength.
Journal ArticleDOI
Modeling environmental factors affecting assimilation of bomb-produced Δ14C in the North Pacific Ocean: Implications for age validation studies
TL;DR: In this article, the authors developed a Bayesian hierarchical model using data sets of bomb-produced radiocarbon in the northeast Pacific Ocean and investigated whether latitude and upwelling exerts an influence on the parameters that describe the rapid Δ14C increase in marine calcium carbonates.
References
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Journal ArticleDOI
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.
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.