Stochastic Relations and the Problem of Prior in the Principle of Maximum Entropy

In this paper we discuss the problem of prior for the maximum entropy principle. We show that stochastic relations can be used to constrain priors and in some case uniquely determine them. The principle of maximum entropy turns stochastic relations into (over)determined systems of partial difference equations for the partition function. All statistical consequences of the stochastic relations are determined by the space of solutions of the system.