发表机构
Duke University; Durham University; Leiden University（杜克大学; 杜伦大学; 莱顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于DALI的框架，超越Fisher近似，解析传播系统失配至参数偏差和后验形变，并在非线性基准中验证，揭示非高斯几何与非加性响应。
AI 中文摘要
我们提出了一个框架，用于在超越高斯Fisher近似的条件下，将系统性数据失配传播为参数偏差和后验形变。利用似然导数近似（DALI），我们推导了最大后验（MAP）点和后验均值的解析表达式，包括系统幅度下的半解析响应展开。我们在一个受控的非线性双参数基准中，将该框架与直接数值计算和马尔可夫链蒙特卡洛（MCMC）采样进行了验证，协方差加权数据空间失配高达$d_{data}=5$。在$d_{data}=5$时，Fisher预测了一个参数偏移的错误方向，并与数值结果相差Fisher度量距离23.1，而解析DALI MAP预测保持在0.091以内，分量误差分别为0.04%和0.46%。响应展开重现了后验均值，误差为0.02%和0.18%，而DALI后验紧密重现了完全采样的非线性后验的位移和形变。同等显著性但方向不同的失配会产生显著不同的参数偏移和后验形变，而多个加性失配可通过非线性推断产生非加性参数响应。通过在系统失配下重建后验，该框架捕捉了参数偏差的非线性响应和非高斯几何：失配如何移动和重塑后验，为何其方向重要，以及如何剖析其组合效应以理解多个系统学之间的相互作用。
英文摘要
We present a framework for propagating systematic data mismatches into parameter biases and posterior deformations beyond the Gaussian Fisher approximation. Using the Derivative Approximation for Likelihoods (DALI), we derive analytic expressions for the maximum a posteriori (MAP) point and posterior mean, including a semi-analytic response expansion in systematic amplitude. We validate the framework against direct numerical calculations and Markov Chain Monte Carlo (MCMC) sampling in a controlled nonlinear two-parameter benchmark up to a covariance-weighted data-space mismatch of $d_{data}=5$. At $d_{data}=5$, Fisher predicts the wrong direction of the shift in one parameter and differs from the numerical result by a Fisher-metric distance of 23.1, whereas the analytic DALI MAP prediction remains within 0.091, with componentwise errors of 0.04% and 0.46%. The response expansion reproduces the posterior mean with errors of 0.02% and 0.18%, while the DALI posterior closely reproduces the displacement and deformation of the fully sampled nonlinear posterior. Mismatches of equal significance but different directions produce markedly different parameter shifts and posterior deformations, while multiple additive mismatches can produce nonadditive parameter responses through nonlinear inference. By reconstructing the posterior under systematic mismatch, the framework captures the nonlinear response and non-Gaussian geometry of parameter bias: how mismatches move and reshape the posterior, why their direction matters, and how their combined effects can be dissected to understand the interplay between multiple systematics.
Comments26 pages, 8 figures, 7 tables
