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

Abstract

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" M0 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 M0=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.

15 pages, 4 figures, accepted in Comp. Phys. Comm

References in corpus (4)

• The fine-grained phase-space structure of Cold Dark Matter halos
• The distribution function of dark matter in massive haloes
• Phase-space structures I: A comparison of 6D density estimators
• FiEstAS sampling -- a Monte Carlo algorithm for multidimensional numerical integration

Cited by in corpus (13)

• Structure Finding in Cosmological Simulations: The State of Affairs
• SubHaloes going Notts: The SubHalo-Finder Comparison Project
• Tracing the Dark Matter Sheet in Phase Space
• The Properties of Cosmic Velocity Fields
• Subhaloes gone Notts: Spin across subhaloes and finders
• Streams Going Notts: The tidal debris finder comparison project
• Statistical Classification Techniques for Photometric Supernova Typing
• Do galaxies form a spectroscopic sequence?
• Subhaloes gone Notts: the clustering properties of subhaloes
• The contribution of star-forming galaxies to the cosmic radio background
• Hydrostatic photoionization models of the Orion Bar
• Dark matter haloes: a multistream view
• HIKER: a halo-finding method based on kernel-shift algorithm