Conditional independence in max-linear Bayesian networks

Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for systems the classical independence results are far from exhausting valid conditional statements. We use tropical algebra derive a compact representation of distribution given partial observation, exploit this obtain complete description all relations. In context-specific case, where is queried relative specific conditioning variables, we introduce notion source DAG disclose context-free case characterize through modified separation concept, $\ast$-separation, combined with eigenvalue condition. also impact graph which describes how events spread deterministically network give characterization such graphs. Our analysis opens up several interesting questions concerning geometry.