Bayesian networks based on max-linear structural equations

22.02.2019 11:15 – 12:15

RESEARCH CENTER FOR STATISTICS SEMINAR / ABSTRACT


We study Bayesian networks based on max-linear structural equations as introduced in [1] and provide a summary of their independence properties. In particular we emphasize that distributions for such networks are in general not faithful to the independence model determined by their associated directed acyclic graph (DAG). We also introduce a new concept, similar to d-separation, for characterising conditional independence by the DAG. In addition, we consider some of the basic issues of estimation and discuss generalised maximum likelihood estimation of the coefficients. Finally we argue that the structure of a minimal network asymptotically can be identified completely from observational data.

[1] Gissibl, N. and Klüppelberg, C. (2018).
Max-linear models on directed acyclic graphs.
Bernoulli 24(4A), 2693–2720.

[2] Lauritzen, S. and Klüppelberg, C. (2017).
Bayesian networks for max-linear models.

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