Preprint Article Version 2 This version is not peer-reviewed

Lagrangian Function on the Finite State Space Statistical Bundle

Version 1 : Received: 26 December 2017 / Approved: 27 December 2017 / Online: 27 December 2017 (10:56:37 CET)
Version 2 : Received: 25 January 2018 / Approved: 26 January 2018 / Online: 26 January 2018 (04:25:24 CET)

A peer-reviewed article of this Preprint also exists.

Pistone, G. Lagrangian Function on the Finite State Space Statistical Bundle. Entropy 2018, 20, 139. Pistone, G. Lagrangian Function on the Finite State Space Statistical Bundle. Entropy 2018, 20, 139.

Journal reference: Entropy 2018, 20, 139
DOI: 10.3390/e20020139

Abstract

The statistical bundle is the set of couples $( Q , W )$ of a probability density Q and a random variable W such that $\mathbb{E}$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.

Subject Areas

information geometry; statistical bundle; lagrangian function