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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Bennett, J., Wakefield, J.: Errors-in-variables in joint population pharmacokinetic/pharmacodynamic. Biometrics 57, 803–812 (2001)
Carrigan, G., Barnett, A., Dobson, A., Mishra, G.: Compensating for missing data from longitudinal studies using WinBUGS. J. Stat. Softw. 19(7), 1–17 (2007)
Carroll, R., Ruppert, D., Stefanski, L.: Measurement error in nonlinear models. Chapman and Hall, New York (2007)
Choi, J., Fuentes, M., Reich, B.J.: Spatial-temporal association between fine particulate matter and daily mortality. J. Comput. Gr. Stat. 53, 2989–3000 (2009)
Gelman, A., Meng, X.: Simulating normalizing constants: from importance sampling to bridge samplingn to path sampling. Stat. Sci. 13(2), 163–185 (1998)
Haining, R., Law, J., Maheswaran, R., Pearson, T., Brindley, P.: Bayesian modelling of environmental risk: example using a small area ecological study of coronary heart disease mortality in relation to modelled outdoor nitrogen. Stoch. Environ. Res. Risk Assess. 21, 501–509 (2007)
He, Y., Zaslavsky, A.: Combining information from cancer registry and medical records data to improve analyses of adjuvant cancer therapies. Biometrics 65, 946–52 (2009)
Heckerman, D., Chickering, D.M., Meek, C., Rounthwaite, R., Kadie, C.M.: Dependency networks for inference, collaborative filtering, and data visualization. J. Mach Learn. Res. 1, 49–75 (2000)
Jackson, C., Best, N., Richardson, S.: Hierarchical related regression for combining aggregate and individual data in studies of socio-economic disease risk factors. J. R. Stat. Soc. Ser A 171(1), 159–178 (2008)
Little, R.: Regression with missing x’s: a review. J. Am. Stat. Assoc. 87, 1227–1237 (1992)
Liu, F., Bayarri, M.J., Berger, J.O.: Modularization in Bayesian analysis, with emphasis on analysis of computer models. Bayesian Anal 4(1), 119–150 (2009)
Lunn, D., Best, N., Spiegelhalter, D., Graham, G., Neuenschwander, B.: Combining MCMC with ‘sequential’ PKPD modelling. J. Pharmacokinet Pharmacodyn. (January 2009). doi:10.1007/s10928-008-9109-1
Maucort-Boulch, D., Franceschi, S., Plummer, M.: International correlation between human papillomavirus prevalence and cervical cancer incidence. Cancer Epidemiol. Biomark. Prev. 17, 717–720 (2008)
Møller, J., Pettitt, A.N., Reeves, R., Berthelsen, K.K.: An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants. Biometrika 93(2), 451–458 (2006)
Mwalili, S., Lesaffre, E., Declerck, D.: A Bayesian ordinal logistic regression model to correct for inter-observer measurement error in a geographical oral health study. J. R. Stat. Soc. Ser. C 54(1), 77–93 (2005)
Neal, R.: Sampling from multimodal distributions using tempered transitions. Stat. Comput. 4, 353–366 (1996)
Raghunathan, T.E., Lepkowski, J.M., Van Hoewyk, J., Solenberger, P.: A multivariate technique for multiply imputing missing values using a sequence of regression models. Survey Methodol. 27, 85–89 (2001)
Richardson, S., Gilks, W.: Conditional independence models for epidemiological studies with covariate measurement error. Stat. Med. 12, 1703–1722 (1993)
Rougier, J.: Comment on paper by Sansó, et al. Bayesian Anal. 3(1), 45–56 (2008)
Scollnick, D.: Bayesian reserving models inspired by chain ladder methods and implemented using WinBUGS. Actuar. Res. Clear. House 2014(2), (2004). http://www.soa.org/news-and-publications/publications/proceedings/arch/pub-arch-detail.aspx
Spiegelhalter, D.J., Thomas, A., Best, N., Lunn, D.: WinBUGS user manual, version 2.0 (2004)
Zhang, L., Beal, S., Sheiner, L.: Simultaneous vs. sequential analysis for population PK/PD data i: best-case performance. J. Pharmacokinet Pharmacodyn. 30, 387–404 (2003a)
Zhang, L., Beal, S., Sheiner, L.: Simultaneous vs. sequential analysis for population PK/PD data ii. J. Pharmacokinet Pharmacodyn. 30, 405–416 (2003b)
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