Bayesian Networks for Max-Linear Models

TY - CHAP

T1 - Bayesian Networks for Max-Linear Models

AU - Klüppelberg, Claudia

AU - Lauritzen, Steffen L.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

M3 - Book chapter

SN - 978-3-030-26813-8

SP - 79

EP - 97

BT - Network Science

A2 - Biagini, Francesca

A2 - Kauermann, Göran

A2 - Meyer-Brandis, Thilo

PB - Springer

ER -