Directed Gaussian graphical models with toric vanishing ideals

Directed Gaussian graphical models are statistical that use a directed acyclic graph (DAG) to represent the conditional independence structures between set of jointly normal random variables. The DAG specifies model through recursive factorization parametrization, via restricted distributions. In this paper, we make an attempt characterize DAGs whose vanishing ideals toric ideals. particular, give some combinatorial criteria construct such from smaller which have An associated monomial map called shortest trek plays important role in our description models. For ideal is toric, prove results about generating sets those