Conditional independence and Markov properties for basic graphs.
In Handbook of Graphical Models
(M. Maathuis, M. Drton, S. Lauritzen, M. Wainwright eds.)
Chapman and Hall/CRC, 2018, pages 3-38.
In this chapter, the concept of conditional independence (CI) is recalled and an overview of
both former and recent results on the description of CI structures is given. The traditional graphical models, namely
those ascribed to undirected graphs (UGs) and directed acyclic graphs (DAGs), can be interpreted
as special cases of statistical models of a CI structure. Therefore, an overview of Markov properties
for these two basic types of graphs is also given.
- AMS classification 68R10, 62H05, 68T30
- conditional independence
- Markov properties
- structural imset
pdf version of a preprint (230kB) is available.