Positivity for Gaussian graphical models |
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| Authors: | Jan Draisma Seth Sullivant Kelli Talaska |
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| Institution: | 1. Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands;2. Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands;3. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA;4. Department of Mathematics, University of California, Berkeley, CA 94720, USA |
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| Abstract: | Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient condition in terms of the graph for when a subdeterminant is zero for all covariance matrices that belong to the Gaussian graphical model. Here we extend this result to give explicit cancellation-free formulas for the expansions of non-zero subdeterminants. |
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| Keywords: | 62H99 05A15 05C90 62J05 |
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