Optimizing Redshift Distribution Inference through Joint Self-Calibration and Clustering-Redshift Synergy

Weilun Zheng, Kwan Chuen Chan, Haojie Xu, Le Zhang, Ruiyu Song
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Abstract

Accurately characterizing the true redshift (true-$z$) distribution of a photometric redshift (photo-$z$) sample is critical for cosmological analyses in imaging surveys. Clustering-based techniques, which include clustering-redshift (CZ) and self-calibration (SC) methods--depending on whether external spectroscopic data are used--offer powerful tools for this purpose. In this study, we explore the joint inference of the true-$z$ distribution by combining SC and CZ (denoted as SC+CZ). We derive simple multiplicative update rules to perform the joint inference. By incorporating appropriate error weighting and an additional weighting function, our method shows significant improvement over previous algorithms. We validate our approach using a DES Y3 mock catalog. The true-$z$ distribution estimated through the combined SC+CZ method is generally more accurate than using SC or CZ alone. To account for the different constraining powers of these methods, we assign distinct weights to the SC and CZ contributions. The optimal weights, which minimize the distribution error, depend on the relative constraining strength of the SC and CZ data. Specifically, for a spectroscopic redshift sample that represents 1% of the photo-$z$ sample, the optimal combination reduces the total error by 20% (40%) compared to using CZ (SC) alone, and it keeps the bias in mean redshift [$\Delta \bar{z} / (1 + z) $] at the level of 0.3%. Furthermore, when CZ data is only available in the low-$z$ range and the high-$z$ range relies solely on SC data, SC+CZ enables consistent estimation of the true-$z$ distribution across the entire redshift range. Our findings demonstrate that SC+CZ is an effective tool for constraining the true-$z$ distribution, paving the way for clustering-based methods to be applied at $z\gtrsim 1$.
通过联合自校准和聚类-红移协同优化红移分布推断
准确描述光度红移(photo-$z$)样本的真实红移(true-$z$)分布对于成像巡天中的宇宙学分析至关重要。基于聚类的技术,包括聚类红移(CZ)和自校准(SC)方法--取决于是否使用外部光谱数据--为此提供了强大的工具。在这项研究中,我们探讨了通过结合 SC 和 CZ(记为 SC+CZ)来联合推断真实的 $z$ 分布。我们推导出简单的乘法更新规则来执行联合推断。通过加入适当的误差加权和额外的加权函数,我们的方法比以前的算法有了显著的改进。我们使用 DES Y3 模拟目录验证了我们的方法。通过 SC+CZ 组合方法估算出的真实 $z$ 分布通常比单独使用 SC 或 CZ 更准确。为了考虑这些方法的不同约束能力,我们为 SC 和 CZ 贡献分配了不同的权重。使分布误差最小化的最佳权重取决于 SC 和 CZ 数据的相对约束强度。具体来说,对于占光电$z$样本1%的光谱红移样本来说,最佳组合比单独使用CZ(SC)减少了20%(40%)的总误差,并将平均红移的偏差[$\Delta \bar{z} / (1 + z) $]保持在0.3%的水平上。此外,当 CZ 数据只能用于低$z$范围,而高$z$范围只能依靠 SC 数据时,SC+CZ 能够在整个红移范围内一致地估计真实的$z$分布。我们的研究结果表明,SC+CZ 是约束真实-$z$分布的有效工具,为基于聚类的方法在$z/gtrsim 1$ 的应用铺平了道路。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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