注意常用的近似值II：估计最佳拟合参数的系统偏倚
Beware of commonly used approximations II: estimating systematic biases in the best-fit parameters
摘要：
宇宙学参数估计从即将到来的实验承诺达到更高的精度比目前的限制。随着统计误差的缩小，对系统误差的控制要求也增加了。因此，迄今为止足够精确的模型或近似值可能会在参数最佳拟合值中引入显着的系统偏差，并危及宇宙学分析的稳健性。我们提出了一个一般的表达式来估计先验的系统误差引入参数推断由于使用不够好的近似在计算的可观察的利益或假设的一个不正确的基础模型。虽然这种方法可以应用于任何科学领域的测量，我们说明了它的权力，通过研究的影响建模角星系功率谱不正确。我们还介绍了多类，一个新的，公共修改的玻尔兹曼代码类，其中包括可能性计算两个不同的示踪剂的角交叉功率谱。我们发现，在大多数的宇宙学参数的显着的偏差，如果一个假设林伯近似或忽略透镜放大率在现代星系巡天分析，和效果一般是较大的多示踪剂的情况下，特别是控制原生非高斯的本地类型的参数，$f_{\rm NL}$。
英文摘要：
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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