Kuo, Kun-Lin; Wang, Yuchung J. Simulating conditionally specified models. (English) Zbl 1490.62018 J. Multivariate Anal. 167, 171-180 (2018). Summary: Expert systems routinely use conditional reasoning. Conditionally specified statistical models offer several advantages over joint models; one is that Gibbs sampling can be used to generate realizations of the model. As a result, full conditional specification for multiple imputation is gaining popularity because it is flexible and computationally straightforward. However, it would be restrictive to require that every regression/classification must involve all of the variables. Feature selection often removes some variables from the set of predictors, thus making the regression local. A mixture of full and local conditionals is referred to as a partially collapsed Gibbs sampler, which often achieves faster convergence due to reduced conditioning. However, its implementation requires choosing a correct scan order. Using an invalid scan order will bring about an incorrect transition kernel, which leads to the wrong stationary distribution. We prove a necessary and sufficient condition for Gibbs sampling to correctly sample the joint distribution. We propose an algorithm that identifies all of the valid scan orders for a given conditional model. A forward search algorithm is discussed. Checking compatibility among conditionals of different localities is also discussed. MSC: 62-08 Computational methods for problems pertaining to statistics 60J22 Computational methods in Markov chains 62H30 Classification and discrimination; cluster analysis (statistical aspects) 65C05 Monte Carlo methods 68T05 Learning and adaptive systems in artificial intelligence Keywords:dependence network; faster convergence; multiple imputation; non-full conditional specification; partially collapsed Gibbs sampler; valid scan order Software:MICE PDFBibTeX XMLCite \textit{K.-L. Kuo} and \textit{Y. J. Wang}, J. 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