论文标题
为什么以及何时在电离时期21-CM功率谱测量时期期望高斯错误分布
Why and When to Expect Gaussian Error Distributions in Epoch of Reionization 21-cm Power Spectrum Measurements
论文作者
论文摘要
我们使用数学分析和数值模拟的组合探索了21-CM功率谱估计器时期的错误分布。我们为目前正在使用的两个估计器中的两个估计器中的单个垃圾箱的误差分布提供了封闭的形式解决方案，我们将其指定为``直接平方''和````直接''和``crossipliplipliply''估计器。然后，我们证明何时应（也不应）具有高斯误差分布，这需要吸引中央限制定理的非标准语句。这对于如何报告上限以及如何根据功率谱测量进行宇宙学推断具有重要意义。具体而言，假设高斯误差分布可以根据估计器的类型而超出或低估上限，并且可以为功率谱而产生过度紧凑的似然函数。
We explore error distributions in Epoch of Reionization 21-cm power spectrum estimators using a combination of mathematical analysis and numerical simulations. We provide closed form solutions for the error distributions of individual bins in 3d-power spectra for two estimators currently in use in the field, which we designate as ``straight-square" and ``cross-multiply" estimators. We then demonstrate when the corresponding spherically binned power spectra should (and should not) have Gaussian error distributions, which requires appealing to nonstandard statements of the central limit theorem. This has important implications for how upper limits are reported, as well as how cosmological inferences are performed based on power spectrum measurements. Specifically, assuming a Gaussian error distribution can over or underestimate the upper limit depending on the type of estimator, and produces overly compact likelihood functions for the power spectrum.
