  The master equation and, more generally, Markov processes are routinely used
as models for stochastic processes. They are often justified on the basis of
randomization and coarse-graining assumptions. Here instead, we derive n-th
order Markov processes and the master equation as unique solutions to an
inverse problem. In particular, we find that when the constraints are not
enough to uniquely determine the stochastic model, the n-th order Markov
process emerges as the unique maximum entropy solution to this otherwise
under-determined problem. This gives a rigorous alternative for justifying such
models while providing a systematic recipe for generalizing widely accepted
stochastic models usually assumed to follow from first principles.
