欧几里得：通过线性构造快速两点相关函数协方差

论文标题

欧几里得：通过线性构造快速两点相关函数协方差

Euclid: Fast two-point correlation function covariance through linear construction

论文作者

Keihanen, E., Lindholm, V., Monaco, P., Blot, L., Carbone, C., Kiiveri, K., Sánchez, A. G., Viitanen, A., Valiviita, J., Amara, A., Auricchio, N., Baldi, M., Bonino, D., Branchini, E., Brescia, M., Brinchmann, J., Camera, S., Capobianco, V., Carretero, J., Castellano, M., Cavuoti, S., Cimatti, A., Cledassou, R., Congedo, G., Conversi, L., Copin, Y., Corcione, L., Cropper, M., Da Silva, A., Degaudenzi, H., Douspis, M., Dubath, F., Duncan, C. A. J., Dupac, X., Dusini, S., Ealet, A., Farrens, S., Ferriol, S., Frailis, M., Franceschi, E., Fumana, M., Gillis, B., Giocoli, C., Grazian, A., Grupp, F., Guzzo, L., Haugan, S. V. H., Hoekstra, H., Holmes, W., Hormuth, F., Jahnke, K., Kümmel, M., Kermiche, S., Kiessling, A., Kitching, T., Kunz, M., Kurki-Suonio, H., Ligori, S., Lilje, P. B., Lloro, I., Maiorano, E., Mansutti, O., Marggraf, O., Marulli, F., Massey, R., Melchior, M., Meneghetti, M., Meylan, G., Moresco, M., Morin, B., Moscardini, L., Munari, E., Niemi, S. M., Padilla, C., Paltani, S., Pasian, F., Pedersen, K., Pettorino, V., Pires, S., Polenta, G., Poncet, M., Popa, L., Raison, F., Renzi, A., Rhodes, J., Romelli, E., Saglia, R., Sartoris, B., Schneider, P., Schrabback, T., Secroun, A., Seidel, G., Sirignano, C., Sirri, G., Stanco, L., Surace, C., Tallada-Crespí, P., Tavagnacco, D., Taylor, A. N., Tereno, I., Toledo-Moreo, R., Torradeflot, F., Valentijn, E. A., Valenziano, L., Vassallo, T., Wang, Y., Weller, J., Zamorani, G., Zoubian, J., Andreon, S., Maino, D., de la Torre, S.

论文摘要

我们提出了一种用Landy-Szalay估计量测量的两点星系相关函数（2PCF）的协方差矩阵快速评估的方法。评估协方差矩阵的标准方法在于在大量模拟目录上运行估计器，并评估其样品协方差。具有较大的随机目录大小（数据与随机对象的比率m >> 1）标准方法的计算成本由计算数据随机和随机随机对的计算成本主导，而估计的不确定性则由数据数据对的不确定性主导。我们提出了一种称为线性构建（LC）的方法，其中估计了大小为M = 1和M = 2的小型随机目录的协方差，并且任意M的协方差构建为它们的线性组合。我们用pinocchio模拟范围r = 20-200 mpc/h验证该方法，并表明协方差估计值是公正的。使用M = 50和2 MPC/H垃圾箱，该方法的理论加速为14。我们讨论对精度矩阵和参数估计的影响，并得出了协方差协方差的公式。

We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy-Szalay estimator. The standard way of evaluating the covariance matrix consists in running the estimator on a large number of mock catalogs, and evaluating their sample covariance. With large random catalog sizes (data-to-random objects ratio M>>1) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs of size M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of these. We validate the method with PINOCCHIO simulations in range r = 20-200 Mpc/h, and show that the covariance estimate is unbiased. With M = 50 and with 2 Mpc/h bins, the theoretical speed-up of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and derive a formula for the covariance of covariance.

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