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

TY - JOUR

T1 - Decision-Oriented Two-Parameter Fisher Information Sensitivity Using Symplectic Decomposition

AU - Yang, Jiannan

N1 - Publisher Copyright: © 2023 The Author(s). Published with license by Taylor & Francis Group, LLC.

PY - 2023/6/27

Y1 - 2023/6/27

N2 - 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.

AB - 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.

KW - Conjugate parameters

KW - Decision under uncertainty

KW - Moment-independent sensitivity

KW - Probabilistic sensitivity

KW - Symplectic eigenvalue

KW - Williamson’s theorem

UR - http://www.scopus.com/inward/record.url?scp=85163031201&partnerID=8YFLogxK

U2 - 10.1080/00401706.2023.2216251

DO - 10.1080/00401706.2023.2216251

M3 - Article

AN - SCOPUS:85163031201

SN - 0040-1706

JO - Technometrics

JF - Technometrics

ER -