论文标题

当心常用近似值II:在最佳拟合参数中估算系统偏见

Beware of commonly used approximations II: estimating systematic biases in the best-fit parameters

论文作者

Bernal, José Luis, Bellomo, Nicola, Raccanelli, Alvise, Verde, Licia

论文摘要

即将进行的实验的宇宙学参数估计有望达到比当前限制更高的精度。随着统计误差的缩小,对系统错误所需的控制增加。因此,到目前为止,足够准确的模型或近似值可能会在参数最佳拟合值中引入明显的系统偏见,并危害宇宙学分析的鲁棒性。我们提出了一个通用表达式,以估算参数推断中引入的系统误差,这是因为在可观察到的感兴趣的计算或假设不正确的基础模型时使用了不足的良好近似值。尽管该方法可以应用于任何科学领域的测量,但我们通过错误地研究角度星系功率谱的效果来说明其功能。我们还介绍了Boltzmann代码类的新公开修改Multi_class,其中包括对两个不同示踪剂计算角跨功能光谱的可能性。我们发现,如果在现代银河系调查分析中假定Ligber近似或忽略透镜放大率,则会引入大多数宇宙学参数,并且对于多跟踪案例的总体而言,其效果通常更大,尤其是对于当地类型的Primordial非高斯的参数,$ f _ f _ $ f_ \ rm nl} $。

Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or approximations that were sufficiently accurate so far, may introduce significant systematic biases in the parameter best-fit values and jeopardize the robustness of cosmological analyses. We present a general expression to estimate a priori the systematic error introduced in parameter inference due to the use of insufficiently good approximations in the computation of the observable of interest or the assumption of an incorrect underlying model. Although this methodology can be applied to measurements of any scientific field, we illustrate its power by studying the effect of modeling the angular galaxy power spectrum incorrectly. We also introduce Multi_CLASS, a new, public modification of the Boltzmann code CLASS, which includes the possibility to compute angular cross-power spectra for two different tracers. We find that significant biases in most of the cosmological parameters are introduced if one assumes the Limber approximation or neglects lensing magnification in modern galaxy survey analyses, and the effect is in general larger for the multi-tracer case, especially for the parameter controlling primordial non-Gaussianity of the local type, $f_{\rm NL}$.

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