Simulating conditionally specified models

Kun Lin Kuo, Yuchung J. Wang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)171-180
Number of pages10
JournalJournal of Multivariate Analysis
StatePublished - Sep 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


  • Dependence network
  • Faster convergence
  • Multiple imputation
  • Non-full conditional specification
  • Partially collapsed Gibbs sampler
  • Valid scan order


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