A Lower Bound for the Fisher Information Measure

TL;DR

This paper introduces a method to approximate the Fisher information measure for complex probabilistic systems by bounding it below using a Gaussian system with matching moments, aiding in practical analysis.

Contribution

It provides a novel lower bound technique for Fisher information based on moment matching, applicable to general parametric probabilistic systems.

Findings

The bound is demonstrated on a practical system.

The technique offers a potentially tight approximation.

It simplifies Fisher information estimation in complex systems.

Abstract

The problem how to approximately determine the absolute value of the Fisher information measure for a general parametric probabilistic system is considered. Having available the first and second moment of the system output in a parametric form, it is shown that the information measure can be bounded from below through a replacement of the original system by a Gaussian system with equivalent moments. The presented technique is applied to a system of practical importance and the potential quality of the bound is demonstrated.