: Received: 26 December 2017 / Approved: 27 December 2017 / Online: 27 December 2017 (10:56:37 CET)
: Received: 25 January 2018 / Approved: 26 January 2018 / Online: 26 January 2018 (04:25:24 CET)
Pistone, G. Lagrangian Function on the Finite State Space Statistical Bundle. Entropy2018, 20, 139.
Pistone, G. Lagrangian Function on the Finite State Space Statistical Bundle. Entropy 2018, 20, 139.
The statistical bundle is the set of couples of a probability density Q and a random variable W such that Q [W] = 0. 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 accelleration 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 of Lagrangian using minus the entropy as potential energy is briefly discussed.
information geometry; statistical bundle; Lagrangian function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.