References
- Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 1970;57:97–109. doi: 10.1093/biomet/57.1.97
- Geman S, Geman D. Stochastic relaxation, Gibbs distribution, and the Bayes restoration of images. IEEE Trans Pattern Anal. 1984;6:721–741. doi: 10.1109/TPAMI.1984.4767596
- Gelfand AE, Smith FM. Sampling-based approaches to calculating marginal densities. J Am Statist Assoc. 1990;85:398–409. doi: 10.1080/01621459.1990.10476213
- Smith AFM, Roberts GO. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. J Roy Stat Soc Ser B. 1993;55:3–23.
- Gilks WR, Richardson S, Spiegelhalter D. Markov chain Monte Carlo in practice. London: Chapman and Hall; 1996.
- Casella G, George E. Explaining the Gibbs sampler. Am Stat. 1992;46:167–174.
- Heckerman D, Chickering DM, Meek C, Rounthwaite R, Kadie C. Dependence networks for inference, collaborative filtering, and data visualization. J Mach Learn Res. 2000;1:49–57.
- Chen SH, Ip EH, Wang Y. Gibbs ensembles for nearly compatible and incompatible conditional models. Comput Stat Data Anal. 2011;55:1760–1769. doi: 10.1016/j.csda.2010.11.006
- Hobert JP, Casella G. Functional compatibility, Markov chains and Gibbs sampling with improper posteriors. J Comput Graph Stat. 1998;7:42–60.
- Liu JS, Wong HW, Kong A. Correlation structure and convergence rate of the Gibbs sampler with various scans. J R Stat Soc Ser B. 1995;57:157–169.
- Liu JS. Discussion on statistical inference and Monte Carlo algorithms, by G. Casella. Test. 1996;5:305–310.
- Van Buuren S, Boshuizen HC, Knook DL. Multiple imputation of missing blood pressure covariates in survival analysis. Stat Med. 1999;18:681–694. doi: 10.1002/(SICI)1097-0258(19990330)18:6<681::AID-SIM71>3.0.CO;2-R
- van Buuren, S, Brand JPL, Groothuis-Oudshoorn CGM, Rubin DB. Fully conditional specification in multivariate imputation. J Stat Comput Sim. 2006;76:1049–1064. doi: 10.1080/10629360600810434
- Rubin DB. Nested multiple imputation of NMES via partially incompatible MCMC. Stat Neerl. 2003;57:3–18. doi: 10.1111/1467-9574.00217
- Schafer JL. Analysis of incomplete multivariate data. London: Chapman and Hall; 1997.
- Rässler S, Rubin DB, Zell ER. Incomplete data in epidemiology and medical statistics. In: Rao CR, Miller JP, Rao DC, editors. Handbook of statistics 27: epidemiology and medical statistics. The Netherlands: Elsevier; 2008. p. 569–601.
- Drechsler J, Rässler S. Does convergence really matter? In: Shalabh and Heumann C, editor. Recent advances in linear models and related areas. Heidelberg: Physica-Verlag; 2008. p. 341–355.
- White IR, Royston P, Wood AM. Multiple imputation using chained equations: Issues and guidance for practice. Stat Med. 2011;30:377–399. doi: 10.1002/sim.4067
- Levine R, Casella G. Optimizing random scan Gibbs samplers. J Multivar Anal. 2006;97:2071–2100. doi: 10.1016/j.jmva.2006.05.008
- Arnold BC, Castillo E, Sarabia JM. Exact and near compatibility of discrete conditional distributions. Comput Stat Data Anal. 2002;40:231–252. doi: 10.1016/S0167-9473(01)00111-6
- Madras N. Lectures on Monte Carlo methods. Providence, RI: American Mathematical Association; 2002.
- Seneta E. Non-negative matrices and Markov Chains. 2nd ed. New York: Springer; 1981.
- Norris JR. Markov Chain. Cambridge: Cambridge University Press; 1998.
- Besag JE. Discussion of Markov Chains for exploring posterior distributions. Ann Stat. 1994;22:1734–1741. doi: 10.1214/aos/1176325752