  We consider the maximum entropy Markov chain inference approach to
characterize the collective statistics of neuronal spike trains, focusing on
the statistical properties of the inferred model. We review large deviations
techniques useful in this context to describe properties of accuracy and
convergence in terms of sampling size. We use these results to study the
statistical fluctuation of correlations, distinguishability and irreversibility
of maximum entropy Markov chains. We illustrate these applications using simple
examples where the large deviation rate function is explicitly obtained for
maximum entropy models of relevance in this field.
