4.7 Article

Estimating multidimensional probability fields using the Field Estimator for Arbitrary Spaces (FiEstAS) with applications to astrophysics

Journal

COMPUTER PHYSICS COMMUNICATIONS
Volume 181, Issue 8, Pages 1436-1441

Publisher

ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2010.04.011

Keywords

Kernel density estimation; Multivariate data analysis

Funding

  1. Spanish Ministerio de Educacion y Ciencia [AYA2007-67965-C03-03]
  2. European Science Foundation (ESF) [ASTROSIM 2027]

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The Field Estimator for Arbitrary Spaces (FiEstAS) computes the continuous probability density field underlying a given discrete data sample in multiple, non-commensurate dimensions. The algorithm works by constructing a metric-independent tessellation of the data space based on a recursive binary splitting. Individual, data-driven bandwidths are assigned to each point, scaled so that a constant mass M(0) is enclosed. Kernel density estimation may then be performed for different kernel shapes, and a combination of balloon and sample point estimators is proposed as a compromise between resolution and variance. A bias correction is evaluated for the particular (yet common) case where the density is computed exactly at the locations of the data points rather than at an uncorrelated set of locations. By default, the algorithm combines a top-hat kernel with M(0) = 2.0 with the balloon estimator and applies the corresponding bias correction. These settings are shown to yield reasonable results for a simple test case, a two-dimensional ring, that illustrates the performance for oblique distributions, as well as for a six-dimensional Hernquist sphere, a fairly realistic model of the dynamical structure of stellar bulges in galaxies and dark matter haloes in cosmological N-body simulations. Results for different parameter settings are discussed in order to provide a guideline to select an optimal configuration in other cases. Source code is available upon request. (C) 2010 Elsevier B.V. All rights reserved.

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