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An explicit link between graphical models and Gaussian Markov random fields on metric graphs

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  • Bolin, David
  • Simas, Alexandre B.
  • Wallin, Jonas

Abstract

We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a Gaussian graphical model. This graphical model has a distribution which is faithful to its pairwise independence graph, that coincides with the neighbor structure of the metric graph. This is used to show that there are no Gaussian random fields on general metric graphs which are both Markov and isotropic in some suitably regular metric on the graph, such as the geodesic or resistance metrics.

Suggested Citation

  • Bolin, David & Simas, Alexandre B. & Wallin, Jonas, 2026. "An explicit link between graphical models and Gaussian Markov random fields on metric graphs," Stochastic Processes and their Applications, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:spapps:v:196:y:2026:i:c:s0304414926000578
    DOI: 10.1016/j.spa.2026.104925
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