Lagrangian Function on the Finite State Space Statistical Bundle

Giovanni Pistone

doi:10.20944/preprints201712.0191.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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)

The statistical bundle is the set of couples

(Q, W)

of a probability density Q and a random variable W such that

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.

information geometry; statistical bundle; lagrangian function

MATHEMATICS & COMPUTER SCIENCE, Probability and Statistics

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Lagrangian Function on the Finite State Space Statistical Bundle

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