Fisher 和 DALI 后验近似用于引力波引力检验

中文摘要 AI 辅助

我们研究了在利用旋进波形中的参数化偏差（TIGER 形式体系）进行广义相对论检验的背景下，基于 Fisher 矩阵及其高阶扩展——似然导数近似（DALI）的引力波（GW）参数估计后验近似的准确性和计算效率。我们采用 IMRPhenomD 波形，并将精确后验采样与以下按复杂度递增顺序排列的近似进行比较：传统 Fisher 矩阵、Fisher 采样（单重 DALI）、双重 DALI 和三重 DALI。我们发现，单重和双重 DALI 均比精确后验显著更快，加速因子在 20 到 1000 之间，具体取决于旋进信噪比——信噪比越大，加速收益越大。对于更完整的波形（如 IMRPhenomHM），这些收益显著更大。为评估近似的准确性，我们使用 Jensen-Shannon 散度。我们得出结论：单重和双重 DALI 均系统地优于标准 Fisher 矩阵近似，而三重 DALI 显示出较大的变异性，限制了其实用优势。我们还引入了一个代码，其中包含 Fisher 和 DALI 分析的新实现（符号 DALI，SymDALI），该代码通过 Wolfram 语言符号计算导数。

英文摘要

We investigate the accuracy and computational efficiency of posterior approximations for gravitational-wave (GW) parameter estimation based on Fisher Matrix and its higher-order extension, the Derivative Approximation for LIkelihoods (DALI), in the context of tests of General Relativity using parameterized deviations in the inspiral waveforms (the TIGER formalism). We adopt the \texttt{IMRPhenomD} waveform and compare the exact posterior sampling to the following approximations in increasing order of complexity: the traditional Fisher Matrix, the Fisher sampling (singlet-DALI), the doublet-DALI and the triplet-DALI. We find that both singlet and doublet-DALI are significantly faster than the exact posterior by factors between 20 and 1000, depending on the inspiral SNRs -- larger gains correspond to larger SNRs. These gains are considerably larger for more complete waveforms, such as \texttt{IMRPhenomHM}. To evaluate the accuracy of the approximations, we use Jensen-Shannon divergence. We conclude that both singlet and doublet-DALI systematically improves over the standard Fisher Matrix approximation, while triplet-DALI shows large variability, limiting its practical advantage. We also introduce a code with a new implementation of Fisher and DALI analysis (Symbolic DALI, \texttt{SymDALI}) which computes derivatives symbolically via \textit{Wolfram Language}.

发表机构

• Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）
• Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）
• Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）

机构由 AI 辅助整理，请以论文原文为准。