  We investigate the maximum caliber variational principle as an inference
algorithm used to predict dynamical properties of complex nonequilibrium,
stationary, statistical systems in the presence of incomplete information.
Specifically, we maximize the path entropy over discrete time step trajectories
subject to normalization, stationarity, and detailed balance constraints
together with a path-dependent dynamical information constraint reflecting a
given average global behavior of the complex system. A general expression for
the transition probability values associated with the stationary random Markov
processes describing the nonequilibrium stationary system is computed. By
virtue of our analysis, we uncover that a convenient choice of the dynamical
information constraint together with a perturbative asymptotic expansion with
respect to its corresponding Lagrange multiplier of the general expression for
the transition probability leads to a formal overlap with the well-known
Glauber hyperbolic tangent rule for the transition probability for the
stochastic Ising model in the limit of very high temperatures of the heat
reservoir.
