Dynamics of the Fisher information metric

Abstract

We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional J[gÎÎ(Îi)], where gÎÎ(Îi) is the Fisher metric. We postulate that this functional of the dynamical variable gÎÎ(Îi) is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to the Fisher information metric. It allows one to impose symmetries on a statistical system in a systematic way. © 2005 The American Physical Society.