Decision-Oriented Two-Parameter Fisher Information Sensitivity Using Symplectic Decomposition

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 a decision-oriented pairing via regrouping or re-parameterization of the FIM. It can be used in tandem with the standard eigenvalue decomposition and offer additional insights into the sensitivity analysis at negligible extra cost. Supplementary materials for this article are available online.

KEYWORDS:

• Conjugate parameters
• Decision under uncertainty
• Moment-independent sensitivity
• Probabilistic sensitivity
• Symplectic eigenvalue
• Williamson’s theorem

Supplementary Materials

The supplementary materials contain details of symplectic decomposition and its computation, proofs that the symplectic egienvectors provides maximization in a symplectic basis, and codes to reproduce Figure 5.

Acknowledgments

For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising. The authors are grateful to Professor Robin Langley, University of Cambridge, for comments on an early draft of this article. We thank referees for their valuable insights and suggestions that led to an improved article.

Data Availability Statement

The datasets generated during and/or analyzed during the current study are available in the GitHub repository: https://github.com/longitude-jyang/SymplecticFisherSensitivity

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

This work has been funded by the Engineering and Physical Sciences Research Council through the award of a Programme Grant “Digital Twins for Improved Dynamic Design,” grant no. EP/R006768.