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Title: A maximum likelihood approach to estimating correlation functions

We define a maximum likelihood (ML for short) estimator for the correlation function, ξ, that uses the same pair counting observables (D, R, DD, DR, RR) as the standard Landy and Szalay (LS for short) estimator. The ML estimator outperforms the LS estimator in that it results in smaller measurement errors at any fixed random point density. Put another way, the ML estimator can reach the same precision as the LS estimator with a significantly smaller random point catalog. Moreover, these gains are achieved without significantly increasing the computational requirements for estimating ξ. We quantify the relative improvement of the ML estimator over the LS estimator and discuss the regimes under which these improvements are most significant. We present a short guide on how to implement the ML estimator and emphasize that the code alterations required to switch from an LS to an ML estimator are minimal.
Authors:
 [1] ;  [2]
  1. Department of Astronomy and Astrophysics, The University of Chicago, Chicago, IL 60637 (United States)
  2. SLAC National Accelerator Laboratory, Menlo Park, CA 94025 (United States)
Publication Date:
OSTI Identifier:
22348532
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 779; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; CATALOGS; CORRELATION FUNCTIONS; DENSITY; MAXIMUM-LIKELIHOOD FIT; RANDOMNESS; UNIVERSE