Dynamics of the Fisher Information Metric

Details Dynamics of the Fisher Information Metric Dynamics of the Fisher Information Metric

2004-10-18

arxiv.org/abs/cond-mat/0410452v1

Phys. Rev. E 71, 056109 (2005)

Physics

Condensed Matter

Statistical Mechanics

11 pages

Scientific paper

10.1103/PhysRevE.71.056109

We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional $J[g^{\mu\nu}(\theta^i)]$, where $g^{\mu\nu}(\theta^i)$ is the Fisher metric. We postulate that this functional of the dynamical variable $g^{\mu\nu}(\theta^i)$ is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to Fisher information metric. It allows to impose symmetries on a statistical system in a systematic way. This work is mainly motivated by the entropy approach to nonmonotonic reasoning.

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