传播 photo-z 不确定性：一种泛函导数方法
Propagating photo-$z$ uncertainties: a functional derivative approach
AI总结：
本文提出用泛函导数计算透镜角功率谱等观测量对源红移分布的敏感度，以高效传播任意形状的 photo-z 小扰动，并在 EUCLID/KV450 场景中验证。
摘要：
测光红移是大尺度结构（LSS）巡天分析与解释中的关键要素。这些红移估计的准确度和精密度直接关系到测光巡天的约束能力。因此，有必要为红移校准定义精密度和准确度要求，以免在最终分析中推断出有偏结果。对于 LSS 的弱引力透镜，测光工作最终体现为估计分析中使用的各个层析分箱内的源红移分布（SRD）。此前关注的重点一直是 SRD 均值的偏移，以及校准必须以多高精度恢复这些偏移。由于估计的 SRD 通常以带相应误差的归一化直方图给出，因此若能相应地传播这些不确定性，以判断给定巡天的要求是否确实得到满足，将是有利的。在此，我们提出使用泛函导数来计算最终观测量（例如透镜角功率谱）对特定红移处 SRD 的敏感度。这使得任意形状的小扰动都可以传播到 SRD，而无需为每个实现再次运行整个分析流程。我们将该方法应用于一项 EUCLID 巡天，并使用 KV450 数据集的 SRD 进行演示，恢复了此前的结果。最后，我们指出，在宇宙剪切分析中传播红移不确定性时，阶数高于二的 SRD 矩可能并不重要。
英文摘要：
Photometric redshifts are a key ingredient in the analysis and interpretation of large-scale structure (LSS) surveys. The accuracy and precision of these redshift estimates are directly linked to the constraining power of photometric surveys. It is hence necessary to define precision and accuracy requirements for the redshift calibration \revision{to not} infer biased results in the final analysis. For weak gravitational lensing of the LSS, the photometry culminates in the estimation of the source redshift distribution (SRD) in each of the tomographic bins used in the analysis. The focus has been on shifts of the mean of the SRDs and how well the calibration must be able to recover those. Since the estimated SRDs are usually given as a normalized histogram with corresponding errors, it would be advantageous to propagate these uncertainties accordingly to see whether the requirements of the given survey are indeed fulfilled. Here we propose the use of functional derivatives to calculate the sensitivity of the final observables, e.g. the lensing angular power spectrum, with respect to the SRD at a specific redshift. This allows the propagation of arbitrarily shaped small perturbations to the SRD, without having to run the whole analysis pipeline for each realization again. We apply our method to an EUCLID survey and demonstrate it with SRDs of the KV450 data set, recovering previous results. Lastly, we note that the moments of the SRD of order larger than two will probably not be relevant when propagating redshift uncertainties in cosmic shear analysis.
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