Information Geometry Description of Inferential Scattering

We investigate the geometrical structure underlying the notion of Inferential Scattering, which was formulated by E. T. Jaynes in the 1980s using the language of equilibrium statistical mechanics. We show that inferential scattering can be naturally defined on a dually flat Riemannian manifold equipped with dual coordinate systems, a differential- geometric structure that occupies a central place in information geometry. We find that the evolution of the system on the dually flat manifold can be expressed as the horizontal lift of an integrable connection. We stress that the notion of inferential scattering has a wide range of applications, being a form of inference and therefore applicable to any statistical system with insufficient information.