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 nth-order Markov processes and the master equation as unique
solutions to an inverse problem. We find that when constraints are not enough to uniquely determine
the stochastic model, an nth-order Markov process emerges as the unique maximum entropy
solution to this otherwise underdetermined 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 the first principles.