Abstract
The cut function defined by the OpenBUGS software is described as a “valve” that prevents feedback in Bayesian graphical models. It is shown that the MCMC algorithm applied by OpenBUGS in the presence of a cut function does not converge to a well-defined limiting distribution. However, it may be improved by using tempered transitions. The cut algorithm is compared with multiple imputation as a gold standard in a simple example.
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Acknowledgments
I started thinking about the cut problem after a presentation by Nicky Best at the IceBUGS meeting in 2006 (http://mathstat.helsinki.fi/openbugs/IceBUGS/Presentations/BestIceBUGS). Over the years, I have had many useful discussions with Nicky Best, Dave Lunn, David Spiegelhalter and Jon Wakefield. I would also like to thank Sylvia Richardson and Nicky Best for inviting me to give a talk on this topic at MCMSki IV.
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Plummer, M. Cuts in Bayesian graphical models. Stat Comput 25, 37–43 (2015). https://doi.org/10.1007/s11222-014-9503-z
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DOI: https://doi.org/10.1007/s11222-014-9503-z