  Markov models are widely used to describe processes of stochastic dynamics.
Here, we show that Markov models are a natural consequence of the dynamical
principle of Maximum Caliber. First, we show that when there are different
possible dynamical trajectories in a time-homogeneous process, then the only
type of process that maximizes the path entropy, for any given singlet
statistics, is a sequence of identical, independently distributed (i.i.d.)
random variables, which is the simplest Markov process. If the data is in the
form of sequentially pairwise statistics, then maximizing the caliber dictates
that the process is Markovian with a uniform initial distribution. Furthermore,
if an initial non-uniform dynamical distribution is known, or multiple
trajectories are conditioned on an initial state, then the Markov process is
still the only one that maximizes the caliber. Second, given a model, MaxCal
can be used to compute the parameters of that model. We show that this
procedure is equivalent to the maximum-likelihood method of inference in the
theory of statistics.
