General methods for monitoring convergence of iterative simulations

By P. Stephen, Brooks, Andrew, Gelman. 1998

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Citations in the corpus

A-NICE-MC: Adversarial Training for MCMC (2017, background): “Another reasonable measurement to consider is Gelman’s R hat diagnostic [36], which evaluates performance across multiple sampled chains.”
A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use (2010, methodology): “MCMC diagnostics, such as trace plots, Geweke Z-statistics (Geweke, 1992) and Brooks-Gelman-Rubin scale reduction statistics (Brooks and Gelman, 1998), indicated rapid convergence and efficient mixing of the chains.”
Updated results on neutrino mass and mass hierarchy from cosmology with Planck 2018 likelihoods (2019, methodology): “We use the Gelman and Rubin statistics [75] to estimate the convergence of the chains.”
QUEST III: An Estimated Open-Economy DSGE Model of the Euro Area with Fiscal and Monetary Policy (2009, methodology): “Convergence of the Markov Chain has been tested by cumulated means and by the diagnostics by Brooks and Gelman (1998). The shape of the likelihood at the posterior mode and the Hessian condition number have been also considered to highlight the lack of identification for some parameters(4). In Table”
Dirichlet Process Mixtures of Generalized Linear Models (2009, methodology): “Further precautions include checking whether the log likelihood of the posterior has “leveled off” or computing parameter variation estimates based on between- and within- sequence variances (Brooks and Gelman, 1998).”
R2WinBUGS: A Package for Running WinBUGS from R (2005, methodology): “If more than one Markov chain is requested and codaPkg is set to FALSE , the convergence diagnostic ˆ R (Brooks and Gelman 1998) is calculated by bugs.sims() for each of the saved parameters.”
Network Meta-Analysis Using R: A Review of Currently Available Automated Packages (2014, methodology): “Convergence was attained based on visual inspection of time-series plots and using the Brooks-Gelman-Rubin test [38].”
Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis (2014, methodology): “Convergence was checked using the Brooks–Gelman–Rubin diagnostic [11], with five chains starting from widely dispersed initial values.”
Massive immigration balances high anthropogenic mortality in a stable eagle owl population: Lessons for conservation (2010, methodology): “We ran two chains and checked the convergence using the Brooks-Gelman-Rubin criterion (Brooks and Gelman, 1998), which indicated convergence (R̂ < 1:005 for all parameters of interest).”
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion (2012, methodology): “To compare the different MCMC methods, we employ the multivariate potential scale reduction factor (MPSRF) diagnostic [6].”
Finite mixture modelling using the skew normal distribution (2007, methodology): “Recently, Brooks and Gelman (1998) provided a generalization of Gelman and Rubin’s method that consider several parameters simultaneously. Suppose there are I independent parallel chains and the length of each chain is 2n. Let θ denote a p × 1 vector of parameters and θi = (θ((1)) i , . . . ,θ (n) i”
A Practical Sequential Stopping Rule for High-Dimensional Markov Chain Monte Carlo (2016, background): “It is also more practical in high-dimensional settings than the popular Gelman–Rubin diagnostic (Gelman and Rubin 1992; Brooks and Gelman 1998), which requires parallel chains. Jones et al. (2006) noted that the GD is based on a Markov chain CLT and hence does not apply more generally than an FWSR t”
Identifying Exoplanets with Deep Learning: A Five-planet Resonant Chain around Kepler-80 and an Eighth Planet around Kepler-90 (2017, methodology): “We tested convergence of the MCMC chains by calculating the Gelman-Rubin potential reduction factor (Gelman & Rubin 1992), which we found to be below 1.2 for all of our parameters (Brooks & Gelman 1998).”