  We formulate a bi-Connection Theory of Gravity whose Gravitational action
consists of a recently defined mutual curvature scalar. Namely, we build a
gravitational theory consisting of one metric and two affine connections, in a
Metric-Affine Gravity setup. Consequently, coupling the two connections on an
equal footing with matter, we show that the geometry of the resulting theory
is, quite intriguingly, that of Statistical Manifold. This ultimately indicates
a remarkable mathematical correspondence between Gravity and Information
Geometry.
