Inference from Iterative Simulation Using Multiple Sequences

By Andrew Gelman, Donald B. Rubin. 1992

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Foundation Posteriors for Approximate Probabilistic Inference (2022, positive): “As a ﬁrst step, we run Metropolis Hastings on one of the six toy programs, and compute R-hat [25].”
A Kernel Test of Goodness of Fit (2016, critical): “This question cannot be answered with classical MCMC convergence statistics, such as the widely used potential scale reduction factor (R-factor) (Gelman & Rubin, 1992) or the effective sample size, since these assume that the Markov chain reaches the true equilibrium distribution i.e. absence of…”
Stan: A Probabilistic Programming Language (2017, methodology): “Before performing output analysis, we recommend generating multiple independent chains in order to more effectively monitor convergence; see (Gelman and Rubin 1992) for more analysis.”
The Problem of Infra-marginality in Outcome Tests for Discrimination (2016, methodology): “five Markov chains in parallel and computed the potential scale reduction factor R̂ (Gelman and Rubin, 1992).”
A global molecular phylogeny of 147 periwinkle species (Gastropoda, Littorininae) (2012, methodology): “Potential scale-reduction factors in all MrBayes analyses were 1.00, showing that runs had converged (Gelman & Rubin 1992) and average standard deviation of split frequencies for partitions with frequency >0.10 in at least one run approached zero.”
Combining full-shape and BAO analyses of galaxy power spectra: a 1.6% CMB-independent constraint on H0 (2020, methodology): “Convergence of the MCMC chains are assessed via the standard Brooks-Gelman and Gelman-Rubin criteria [75, 76].”
Efficient identification of exoplanetary transit candidates from SuperWASP light curves (2007, methodology): “After discarding the first 500 steps we compared the variances within and between five independent sub-chains, using the test statistic of Gelman & Rubin (1992).”
Gaussian Process Structural Equation Models with Latent Variables (2010, methodology): “Following Lee (2007), we evaluate convergence using the EPSR statistic (Gelman and Rubin, 1992), which compares the variability of a given marginal posterior within each chain and between chains.”
Robustness of Hierarchical Modeling of Skill Association in Cognitive Diagnosis Models (2008, methodology): “Across all simulation conditions and within the real data analysis, MCMC convergence was determined on the basis of the Gelman and Rubin diagnostic (R̂; Gelman & Rubin, 1992) and by visual inspection of each parameter’s MCMC time-series plot and graphed posterior distribution.”
A Hierarchical IRT Model for Criterion-Referenced Measurement (2000, methodology): “There is currently no general agreement on a method for determining convergence of the Gibbs sampler (see, e.g., Gelman & Rubin, 1992; Zellner & Min, 1995).”
Why environmental scientists are becoming Bayesians (2004, background): “Although there are number of indices to help gauge convergence (e.g. Gelman & Rubin 1992), for complex models one may never be completely sure.”
Territoriality, Social Bonds, and the Evolution of Communal Signaling in Birds (2016, unknown): “We checked convergence of model parameters (ﬁxed eﬀects and random eﬀects) using the Gelman-Rubin statistic (the potential scale reduction, PSR, factor should be < 1.1 among chains (Gelman and Rubin, 1992); all PSR factors met this criterion).”