Statistics Colloquium

Title: Gaussian DAG models with symmetries

Abstract:   A Gaussian DAG model is a family of multivariate normal distributions where the structure of zero elements of the Cholesky factor, that is the triangular matrix obtained by the Cholesky decomposition of the covariance matrix, is determined by a directed acyclic graph (DAG). In this talk I introduce a new subclass of Gaussian DAG models by imposing additional restrictions on the elements of the Cholesey factor. This is motivated by a recent paper of Lauritzen and Højsgaard where similar subclass of graphical Gaussian models with edge and vertex symmetries were introduced. I will explain how these restricted DAG models are naturally represented by color graphs and discuss the estimation problem.

In particular, I will focus on the maximum likelihood estimation of the parameters.