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

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 i...

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Bibliographic Details
Published in:Technometrics 2024-01, Vol.66 (1), p.28-39
Main Author: Yang, Jiannan
Format: Article
Language:English
Subjects:
Conjugate parameters
Cost analysis
Decision making
Decision under uncertainty
Decomposition
Eigenvalues
Eigenvectors
Fisher information
Matrix
Moment-independent sensitivity
Parameter sensitivity
Parameterization
Probabilistic sensitivity
Sensitivity analysis
Symplectic eigenvalue
Williamson's theorem
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Summary: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.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.2023.2216251