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