FUNDAMENTAL EQUATIONS FOR STATISTICAL SUBMANIFOLDS WITH APPLICATIONS TO THE BARTLETT CORRECTION

摘要: Many applications of Amari's dual geometries involve one or more submanifolds imbedded in a supermanifold. In the differential geometry literature, there is set equations that describe relationships between invariant quantities on submanifold and supermanifold when Riemannian connection used. We extend these to statistical manifolds, manifolds which pair connections defined. The found include mean curvature are used calculations involving such topics as information loss efficiency. As an application equations, Bartlett correction interpreted terms curvatures other quantities.