论文标题
提高两点相关函数的估计器的精度
Improving the accuracy of estimators for the two-point correlation function
论文作者
论文摘要
我们展示了如何在不牺牲效率的情况下提高两点相关函数估计值的准确性。我们通过将它们与精确的参考值进行比较来量化配对计数和Landy-Szalay估计器的误差。使用随机点集的标准方法与使用准蒙特斯〜CARLO集成的几何动机估计器和估计器进行了比较。在标准方法中，错误将比例比例为$ 1/\ sqrt {n_r} $，而$ n_r $是随机点的数量。在我们的改进方法中，错误几乎比例地缩放到$ 1/n_q $，其中$ n_q $是低轴repancy序列中的点数。与标准估计器相比，我们研究了新估计器的运行时间，并保持相同的准确性。对于被考虑的情况，我们总是看到速度从50％到数千倍的速度不等。我们还讨论了如何将这些改进的估计量应用于未完全采样的星系目录。
We show how to increase the accuracy of estimates of the two-point correlation function without sacrificing efficiency. We quantify the error of the pair-counts and of the Landy-Szalay estimator by comparing them with exact reference values. The standard method, using random point sets, is compared to geometrically motivated estimators and estimators using quasi-Monte~Carlo integration. In the standard method, the error scales proportionally to $1/\sqrt{N_r}$, with $N_r$ being the number of random points. In our improved methods, the error scales almost proportionally to $1/N_q$, where $N_q$ is the number of points from a low-discrepancy sequence. We study the run times of the new estimator in comparison to those of the standard estimator, keeping the same level of accuracy. For the considered case, we always see a speedup ranging from 50% up to a factor of several thousand. We also discuss how to apply these improved estimators to incompletely sampled galaxy catalogues.
