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Bayesian Networks for Max-Linear Models

  • Claudia KlüppelbergEmail author
  • Steffen Lauritzen
Chapter

Abstract

We study Bayesian networks based on max-linear structural equations as introduced in Gissibl and Klüppelberg (2018) and provide a summary of their independence properties. In particular, we emphasize that distributions for such networks are generally not faithful to the independence model determined by their associated directed acyclic graph. In addition, we consider some of the basic issues of estimation and discuss generalized maximum likelihood estimation of the coefficients, using the concept of a generalized likelihood ratio for non-dominated families as introduced by Kiefer and Wolfowitz (1956). Finally, we argue that the structure of a minimal network asymptotically can be identified completely from observational data.

Notes

Acknowledgements

The authors have benefited from discussions with Nadine Gissibl and financial support from the Alexander von Humboldt Stiftung.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Center for Mathematical SciencesTechnical University of MunichMunichGermany
  2. 2.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark

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