论文标题
使用符号分解的面向决策的两参数Fisher信息敏感性
Decision-oriented two-parameter Fisher information sensitivity using symplectic decomposition
论文作者
论文摘要
Fisher Information Matrix（FIM）的特征值和特征向量可以揭示系统中最敏感的方向，并且在科学和工程中具有广泛的应用。我们为FIM提出了特征值分解的符号变体，并针对两参数共轭对提取灵敏度信息。符号方法将FIM分解到均匀的符号基础上。这种符合性结构可以揭示两参数对之间的其他灵敏度信息，否则以正交基础隐藏在标准特征值分解中。提出的灵敏度方法可以应用于自然配对的两参数分布参数，或通过重组或重新参数化FIM来实现决策的配对。它可以与标准特征值分解一起使用，并以可忽略的额外成本提供对灵敏度分析的更多见解。
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.
