Finding the minimal set for collapsible graphical models

Wang, Xiaofei; Guo, Jianhua; He, Xuming

doi:10.1090/S0002-9939-2010-10509-9

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.

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