An empirical approach to model selection: weak lensing and intrinsic alignments
An empirical approach to model selection: weak lensing and intrinsic alignments
复制标题
模型选择的实证方法：弱透镜效应和内在对准
DOI：
10.1093/mnras/stad2213
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发表时间：
2023
影响因子：
4.8
通讯作者：
Mandelbaum, R.
中科院分区：
文献类型：
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作者：
Campos, A.;Samuroff, S.;Mandelbaum, R.
在宇宙学中，我们通常会在模型之间进行选择来描述我们的数据，并且可能会由于模型不足而产生偏差，或者由于模型过于复杂而失去约束力。在本文中，我们提出了一种模型选择的经验方法，该方法明确平衡参数偏差与模型复杂性。我们的方法使用合成数据来校准模型之间的偏差和 χ2 差异之间的关系。这使我们能够解释从真实数据获得的 χ2 值（即使目录是盲的）并相应地选择模型。我们将我们的方法应用于内在对准问题——最重要的弱透镜系统之一，也是现代透镜测量中误差预算的主要贡献者。具体来说，我们考虑第三年暗能量勘测 (DES Y3) 的例子，并比较常用的非线性对准 (NLA) 和潮汐对准和潮汐扭矩 (TATT) 模型。这些模型针对 Ωm–S8 平面中的偏差进行校准。一旦考虑了噪声，我们发现可以设置一个阈值 Δχ2，以保证使用 NLA 的分析在某些指定的 Nσ 水平和置信水平上是无偏的。相比之下，我们发现理论上定义的阈值（例如基于 χ2 的 p 值）往往过于乐观，并且不能可靠地排除高达~1-2σ 的宇宙学偏差。考虑到真实的 DES Y3 宇宙剪切结果，根据 NLA 和 TATT 分析报告的 χ2 差异，我们发现如果 NLA 为基准模型，结果可能会（在 Ωm-S8 平面上）偏差超过 0.3σ。更广泛地说，我们在这里提出的方法简单且通用，并且需要相对较低的资源。我们预计未来的分析将作为许多情况下的模型选择工具的应用。
In cosmology, we routinely choose between models to describe our data, and can incur biases due to insufficient models or lose constraining power with overly complex models. In this paper, we propose an empirical approach to model selection that explicitly balances parameter bias against model complexity. Our method uses synthetic data to calibrate the relation between bias and the χ2difference between models. This allows us to interpret χ2values obtained from real data (even if catalogues are blinded) and choose a model accordingly. We apply our method to the problem of intrinsic alignments – one of the most significant weak lensing systematics, and a major contributor to the error budget in modern lensing surveys. Specifically, we consider the example of the Dark Energy Survey Year 3 (DES Y3), and compare the commonly used non-linear alignment (NLA) and tidal alignment and tidal torque (TATT) models. The models are calibrated against bias in the Ωm–S8plane. Once noise is accounted for, we find that it is possible to set a threshold Δχ2that guarantees an analysis using NLA is unbiased at some specified levelNσ and confidence level. By contrast, we find that theoretically defined thresholds (based on, e.g.p-values for χ2) tend to be overly optimistic, and do not reliably rule out cosmological biases up to ∼1–2σ. Considering the real DES Y3 cosmic shear results, based on the reported difference in χ2from NLA and TATT analyses, we find a roughlychance that were NLA to be the fiducial model, the results would be biased (in the Ωm–S8plane) by more than 0.3σ. More broadly, the method we propose here is simple and general, and requires a relatively low level of resources. We foresee applications to future analyses as a model selection tool in many contexts.