Finding the minimal set for collapsible graphical models
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- by Xiaofei Wang, Jianhua Guo and Xuming He PDF
- Proc. Amer. Math. Soc. 139 (2011), 361-373 Request permission
Abstract:
A graphical model is said to be collapsible onto a set of variables if the implied model for the marginal distribution of those variables is the same as that given by the induced subgraph. We discuss the notion of collapsibility under multinomial, Gaussian, and mixed graphical models for undirected graphs, and we show that there exists a unique minimal set of variables onto which a graphical model can be collapsed. We also provide a useful algorithm for finding the minimal set and give examples to illustrate the utility of using collapsibility.References
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Additional Information
- Xiaofei Wang
- Affiliation: Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin Province, People’s Republic of China
- Email: mathswangxiaofei@yahoo.com.cn
- Jianhua Guo
- Affiliation: Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin Province, People’s Republic of China
- Email: jhguo@nenu.edu.cn
- Xuming He
- Affiliation: Department of Statistics, University of Illinois, 725 S. Wright Street, Champaign, Illinois 61820
- Email: x-he@uiuc.edu
- Received by editor(s): April 4, 2009
- Received by editor(s) in revised form: March 19, 2010
- Published electronically: July 21, 2010
- Additional Notes: This research was supported by the National Natural Science Foundation of China (Grants No. 10701022, 10871038, 10828102 and 10926186), the National 973 Key Project of China (2007CB311002), and the U.S. National Science Foundation award DMS-0630950
- Communicated by: Edward C. Waymire
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 361-373
- MSC (2000): Primary 62-09, 05E05; Secondary 05C85
- DOI: https://doi.org/10.1090/S0002-9939-2010-10509-9
- MathSciNet review: 2729097