Information geometry for bivariate distribution control

The optimal control of stochastic processes through sensor estimation of probability density functions has a geometric setting via information theory and the information metric. Information theory identifies the exponential distribution as the maximum entropy distribution if only the mean is known and the gamma distribution if also the mean logarithm is known. Previously, we used the surface representing gamma models to provide an appropriate structure on which to represent the dynamics of a univariate process and algorithms to control it. In this paper we extend these procedures to gamma models with positive correlation, for which the information theoretic 3-manifold geometry has recently been formulated. For comparison we summarize also the case for bivariate Gaussian processes with arbitrary correlation.