  We elaborate the notion of a Ricci curvature lower bound for parametrized
statistical models. Following the seminal ideas of Lott-Strum-Villani, we
define this notion based on the geodesic convexity of the Kullback-Leibler
divergence in a Wasserstein statistical manifold, that is, a manifold of
probability distributions endowed with a Wasserstein metric tensor structure.
Within these definitions, the Ricci curvature is related to both, information
geometry and Wasserstein geometry. These definitions allow us to formulate
bounds on the convergence rate of Wasserstein gradient flows and information
functional inequalities in parameter space. We discuss examples of Ricci
curvature lower bounds and convergence rates in exponential family models.
