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Simulating conditionally specified models

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  • Kuo, Kun-Lin
  • Wang, Yuchung J.

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.

Suggested Citation

  • Kuo, Kun-Lin & Wang, Yuchung J., 2018. "Simulating conditionally specified models," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 171-180.
  • Handle: RePEc:eee:jmvana:v:167:y:2018:i:c:p:171-180
    DOI: 10.1016/j.jmva.2018.04.012
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    References listed on IDEAS

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    1. Gelman A., 2004. "Parameterization and Bayesian Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 537-545, January.
    2. A. Gelman & T. P. Speed, 1999. "Corrigendum: Characterizing a joint probability distribution by conditionals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 483-483, April.
    3. van Dyk, David A. & Park, Taeyoung, 2008. "Partially Collapsed Gibbs Samplers: Theory and Methods," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 790-796, June.
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