小心常用的近似I：预测中的错误
Beware of commonly used approximations I: errors in forecasts
摘要：
在精确宇宙学时代，确定宇宙学参数中统计误差的正确大小至关重要。然而，在星系巡天分析中广泛使用的近似值可能导致参数不确定性，即使在理论很好理解的情况下（例如，线性尺度）。这些近似可以在三个不同的层次上引入：以可能性的形式，在可观察的理论建模和可观察的数值计算。它们的结果在数据分析中都很重要，例如，马尔可夫链蒙特卡罗参数推断，以及何时设计观测工具和策略，预测它们对宇宙学参数的约束能力，例如使用Fisher矩阵分析。在这项工作中，考虑到星系的角功率谱作为目标观测，我们报告了一个例子，这样的三个类别的近似：忽略非对角项的协方差矩阵，忽略宇宙放大率和使用Limber近似大尺度。我们发现，这些常用的近似影响分析的鲁棒性，并导致，也许违反直觉，无法接受的大错误估计的参数误差（从几个~$10\%$到几个~$100\%$）和相关性。此外，这些近似甚至可能破坏新生的多示踪剂和多信使宇宙学的好处。因此，我们建议对调查设计或数据分析中采用的每种近似值重复进行此处介绍的分析类型，以量化其对结果的影响。为此，我们开发了\texttt{Multi\_CLASS}，一个新的扩展\texttt{CLASS}，其中包括多个（星系和其他示踪剂，如引力波）人口的角功率谱。
英文摘要：
In the era of precision cosmology, establishing the correct magnitude of statistical errors in cosmological parameters is of crucial importance. However, widely used approximations in galaxy surveys analyses can lead to parameter uncertainties that are grossly mis-estimated, even in a regime where the theory is well understood (e.g., linear scales). These approximations can be introduced at three different levels: in the form of the likelihood, in the theoretical modelling of the observable and in the numerical computation of the observable. Their consequences are important both in data analysis through e.g., Markov Chain Monte Carlo parameter inference, and when survey instrument and strategy are designed and their constraining power on cosmological parameters is forecasted, for instance using Fisher matrix analyses. In this work, considering the galaxy angular power spectrum as the target observable, we report one example of approximation for each of such three categories: neglecting off-diagonal terms in the covariance matrix, neglecting cosmic magnification and using the Limber approximation on large scales. We show that these commonly used approximations affect the robustness of the analysis and lead, perhaps counter-intuitively, to unacceptably large mis-estimates of parameters errors (from few~$10\%$ up to few~$100\%$) and correlations. Furthermore, these approximations might even spoil the benefits of the nascent multi-tracer and multi-messenger cosmology. Hence we recommend that the type of analysis presented here should be repeated for every approximation adopted in survey design or data analysis, to quantify how it may affect the results. To this aim, we have developed \texttt{Multi\_CLASS}, a new extension of \texttt{CLASS} that includes the angular power spectrum for multiple (galaxy and other tracers such as gravitational waves) populations.
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