Lagrangian Function on the Finite State Space Statistical Bundle

The statistical bundle is the set of couples ([Formula: see text]) of a probability density Q and a random variable W such that [Formula: see text]. On a finite state space, we assume Q to be a probability density with respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is a model for Information Geometry. Velocity and acceleration of a one-dimensional statistical model are computed in this set up. The Euler–Lagrange equations are derived from the Lagrange action integral. An example Lagrangian using minus the entropy as potential energy is briefly discussed.