Demonstration of Enhanced Monte Carlo Computation of the Fisher Information for Complex Problems

TL;DR

This paper reviews and demonstrates enhanced Monte Carlo methods, including feedback-based and perturbation approaches, for accurately estimating the Fisher information matrix in complex problems where closed-form solutions are unavailable.

Contribution

It introduces and compares improved Monte Carlo techniques for Fisher information estimation, demonstrating their effectiveness over basic resampling methods.

Findings

Enhanced accuracy of Fisher information estimates with proposed methods

Numerical examples validate the improvements over traditional approaches

Summarized relevant theoretical background

Abstract

The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest. There are many applications of the information matrix in statistical modeling, system identification and parameter estimation. This short paper reviews a feedback-based method and an independent perturbation approach for computing the information matrix for complex problems, where a closed form of the information matrix is not achievable. We show through numerical examples how these methods improve the accuracy of the estimate of the information matrix compared to the basic resampling-based approach. Some relevant theory is summarized.