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Factorization of posteriors and partial imputation algorithm for graphical models with missing data

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  • Geng, Zhi
  • Li, Kaican

Abstract

In this paper, we discuss factorization of a posterior distribution and present a partial imputation algorithm for a graphical model with incomplete data. We use an ordinary graph to represent a graphical model and introduce a hypergraph to represent an observed data pattern where each hyperedge is a set of variables observed for a group of individuals. First, in terms of a decomposition of such a mixed graph, we discuss factorization of a joint posterior distribution into several marginal posterior distributions so that calculation of posterior distribution can be localized. Then, for a mixed graph which cannot be decomposed without loss of information, we present a partial imputation algorithm which imputes only a part of missing data and reduces unnecessary imputation of an ordinary Gibbs sampler. Finally, we discuss the efficiency improved by a decomposition and the partial imputation algorithm.

Suggested Citation

  • Geng, Zhi & Li, Kaican, 2003. "Factorization of posteriors and partial imputation algorithm for graphical models with missing data," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 369-379, October.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:4:p:369-379
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    References listed on IDEAS

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    1. Zhi Geng & Kang Wan & Feng Tao, 2000. "Mixed Graphical Models with Missing Data and the Partial Imputation EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 433-444, September.
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    Cited by:

    1. Geng, Zhi & Wang, Chi & Zhao, Qiang, 2005. "Decomposition of search for v-structures in DAGs," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 282-294, October.
    2. Ng, Kai Wang & Tang, Man-Lai & Tan, Ming & Tian, Guo-Liang, 2008. "Grouped Dirichlet distribution: A new tool for incomplete categorical data analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 490-509, March.

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