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 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.
Cite
@article{arxiv.2207.12077,
title = {Decision-oriented two-parameter Fisher information sensitivity using symplectic decomposition},
author = {Jiannan Yang},
journal= {arXiv preprint arXiv:2207.12077},
year = {2023}
}
Comments
15 pages, 10 figures, and a Supplement Material as ancillary files. Technometrics 2023. New version adds a benchmark section. The datasets generated during and/or analysed during the current study are available in the GitHub repository: https://github.com/longitude-jyang/SymplecticFisherSensitivity