Simulating conditionally specified models

Kun-Lin Kuo and Yuchung J. Wang

Journal of Multivariate Analysis, 2018, vol. 167, issue C, 171-180

Abstract: 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.

Keywords: Dependence network; Faster convergence; Multiple imputation; Non-full conditional specification; Partially collapsed Gibbs sampler; Valid scan order (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.jmva.2018.04.012

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