Kullback’s inequality and Cramer Rao bounds for point process models

Abstract

<p>A lower bound on the Kullback-Leibler divergence known as Kullback’s inequality can be determined with the Legendre transform of the cumulant generating function. The Cramer Rao bound can be derived from Kullback’s inequality as the inverse of the second order term in a Taylor expansion. Analogous forms for Kullback’s inequality and the Cram er</p><p>Rao bound for point processes were recently derived using functional methods from quantum field theory. This article develops Kullback’s inequality and the Cramer Rao bound for point process parametrisations as performance bounds for models used in multi-object filtering.</p>