Decision-oriented two-parameter Fisher information sensitivity using symplectic decomposition

TL;DR

This paper introduces a symplectic eigenvalue decomposition method for the Fisher information matrix that reveals detailed sensitivity information between two-parameter pairs, enhancing traditional analysis with minimal additional computational cost.

Contribution

It proposes a novel symplectic decomposition of the FIM to uncover inter-parameter sensitivity details not accessible through standard eigenvalue methods.

Findings

Reveals additional sensitivity insights between parameter pairs

Applicable to paired or re-parameterized distributions

Provides enhanced sensitivity analysis with negligible extra cost

Abstract

The eigenvalues and eigenvectors of the Fisher information matrix (FIM) can reveal the most and least sensitive directions of a system and it has wide application across science and engineering. We present a symplectic variant of the eigenvalue decomposition for the FIM and extract the sensitivity information with respect to two-parameter conjugate pairs. The symplectic approach decomposes the FIM onto an even-dimensional symplectic basis. This symplectic structure can reveal additional sensitivity information between two-parameter pairs, otherwise concealed in the orthogonal basis from the standard eigenvalue decomposition. The proposed sensitivity approach can be applied to naturally paired two-parameter distribution parameters, or decision-oriented pairing via re-grouping or re-parameterization of the FIM. It can be utilised in tandem with the standard eigenvalue decomposition and offer additional insight into the sensitivity analysis at negligible extra cost.