We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional J[g µν (θ i)], where g µν (θ i) is the Fisher metric. We postulate that this functional of the dynamical variable g µν (θ 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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