On the Consistency of Maximum Likelihood Estimators for Causal Network Identification

We consider the problem of identifying parameters a particular class Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure any BAR model is encoded by directed graph. Incoming edges to node in graph indicate that state at time instant influenced states corresponding parental nodes previous instant. associated edge weights determine level influence from each node. In simplest setup, parameter node's variable convex combination and an additional noise random variable. This letter focuses on weight identification using Maximum Likelihood (ML) estimation proves ML estimator strongly consistent for two variants model. additionally derive closed-form estimators aforementioned prove their strong consistency.