*Hypertree MSDAG: Top Level Structure of a MSBN
Defi: Let D be the union of Di (i=1,…,n) where each Di is a connected DAG. D is a hypertree MSDAG if it is a DAG built by the following procedure:
- Start with an empty graph. Recursively add a DAG Di called a hypernode, to the existing MSDAG subject to the constraints:
- [d-sepset] For each Dj (j<k), Ijk =Nj?Nk is a d-sepset when the two DAGs are isolated.
- [Local covering] There exists Di (I<k) such that, for each Dj (j<k;j?i), Ijk ? Ni . For such Di, Iik is called the hyperlink b/w hypernodes Di and Dk.
Semantics: Each hyperlink renders the two parts of the MSBN that it connects conditionally independent.