Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review

Cowles, Mary Kathryn; Carlin, Bradley P.

doi:10.2307/2291683

Cited by 787 publications

(738 citation statements)

References 0 publications

Supporting

Mentioning

718

Contrasting

Unclassified

Order By: Relevance

“…Unfortunately, it is not always easy to determine when convergence has been achieved, as emphasized by Kass et al (1998). Cowles and Carlin (1996) provide a description of the various tests and diagnostics that have been proposed. For example, Gelman and Rubin (1992) suggest starting the Gibbs sampler from several different points and testing the hypothesis that the statistic of interest (in our case, the posterior mean) is the same when calculated from each of the presumably converged sequences.…”

Section: Hierarchical Bayes For Mixed Logitmentioning

confidence: 99%

Discrete Choice Methods with Simulation

Train¹

2003

3,790

2,450

View full text Add to dashboard Cite

Section: Hierarchical Bayes For Mixed Logitmentioning

confidence: 99%

Discrete Choice Methods with Simulation

Train¹

2003

3,790

2,450

View full text Add to dashboard Cite

“…More objective measures have been developed to determine whether a Markov chain has converged, but are usually more difficult to implement and can be computationally expensive. There is quite a large number of these methods and they vary in their applicability to different sampling problems (see Brooks & Roberts, 1998;Mengersen et al, 1999;Cowles & Carlin, 1996 for reviews).…”

Section: Cautions and Recommendationsmentioning

confidence: 99%

Uncovering mental representations with Markov chain Monte Carlo

Sanborn

Griffiths

Shiffrin

2010

Cognitive Psychology

View full text Add to dashboard Cite

A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription. Richard M. Shiffrin Indiana University, Bloomington Abstract A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these functions. Our approach uses people as components of a Markov chain Monte Carlo (MCMC) algorithm, a sophisticated sampling method originally developed in statistical physics. Experiments 1 and 2 verified the MCMC method by training participants on various category structures and then recovering those structures. Experiment 3 demonstrated that the MCMC method can be used estimate the structures of the real-world animal shape categories of giraffes, horses, dogs, and cats. Experiment 4 combined the MCMC method with multidimensional scaling to demonstrate how different accounts of the structure of categories, such as prototype and exemplar models, can be tested, producing samples from the categories of apples, oranges, and grapes.

show abstract

“…The convergence of MCMC-sampling (see e.g. Cowles 1996) was examined using Geweke Z-score (Geweke 1992), Gelman Rubin's convergence diagnostics (Cowles 1996) and also with looking autocorrelations in MCMC-chains.…”

Section: Discussionmentioning

confidence: 99%

“…Cowles 1996) in estimation of Bayesian logistic regression was examined using Geweke Z-score (Geweke 1992), Gelman Rubin's convergence diagnostics (Cowles 1996) and also with looking autocorrelations in MCMCchains (model parameters) in lags 1, 5, 10, 25 and 50. The Geweke Z-scores (first fraction was 10% and second 50%) The cases where Geweke Z-scores indicate non-convergence at the same time chains are determined converged using Gelman and Rubin's test.…”

Section: Cluster Occurrence Explained By Background Factorsmentioning

confidence: 99%