Some results on the Gaussian Markov Random Field construction problem based on the use of invariant subgraphs

Abstract The study of Gaussian Markov Random Fields has attracted the attention a large number scientific areas due to its increasing usage in several fields application. Here, we consider construction from graph and positive-definite matrix, which is closely related problem finding Maximum Likelihood Estimator covariance matrix underlying distribution. In particular, it simultaneously required that variances covariances between variables associated with adjacent nodes are fixed by pairs non-adjacent conditionally independent given all other variables. solution this exists unique up choice vector means. paper, some results focusing on certain type subgraphs (invariant subgraphs) representation Field as Multivariate presented. These ease computation aforementioned problem.