Related papers: Improving the accuracy of estimators for the two-p…
Measuring the two-point correlation function of the galaxies in the Universe gives access to the underlying dark matter distribution, which is related to cosmological parameters and to the physics of the primordial Universe. The estimation…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
Nine of the most important estimators known for the two-point correlation function are compared using a predetermined, rigorous criterion. The indicators were extracted from over 500 subsamples of the Virgo Hubble Volume simulation cluster…
The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the…
All estimators of the two-point correlation function are based on a random catalogue, a set of points with no intrinsic clustering following the selection function of a survey. High-accuracy estimates require the use of large random…
A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to…
The two-point correlation function (2PCF) is a cornerstone of precision cosmology, yet its estimation from imaging surveys is vulnerable to contamination and incompleteness arising from imperfect target selection and pipeline-level…
We define a Maximum Likelihood (ML for short) estimator for the correlation function, {\xi}, that uses the same pair counting observables (D, R, DD, DR, RR) as the standard Landy and Szalay (1993, LS for short) estimator. The ML estimator…
Second-order measures, such as the two-point correlation function, are geometrical quantities describing the clustering properties of a point distribution. In this article well-known estimators for the correlation integral are reviewed and…
Two-point correlation functions (2PCF) are widely used to characterize how points cluster in space. In this work, we study the problem of measuring the 2PCF over a large set of points, restricted to a subset satisfying a property of…
The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…
Using the pair-count implementaion from the Corrfunc package we show that with a low discrepency sequence we can calculate the two-point correlation function more accurately than with random points at no extra computational cost.
We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small…
Galaxy redshift surveys are subject to incompleteness and inhomogeneous sampling due to the various constraints inherent to spectroscopic observations. This can introduce systematic errors on the summary statistics of interest, which need…
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…
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…
We have developed a new analytic method to calculate the galaxy two-point correlation functions (TPCFs) accurately and efficiently, applicable to surveys with finite, regular, and mask-free geometries. We have derived simple, accurate…
As we move towards future galaxy surveys, the three-point statistics will be increasingly leveraged to enhance the constraining power of the data on cosmological parameters. An essential part of the three-point function estimation is…
We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point…
We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and…