  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.
