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The Field Estimator for Arbitrary Spaces (FiEstAS) computes the continuousprobability density field underlying a given discrete data sample in multiple,non-commensurate dimensions. The algorithm works by constructing ametric-independent tessellation of the data space based on a recursive binarysplitting. Individual, data-driven bandwidths are assigned to each point,scaled so that a constant "mass" M0 is enclosed. Kernel density estimation maythen be performed for different kernel shapes, and a combination of balloon andsample point estimators is proposed as a compromise between resolution andvariance. A bias correction is evaluated for the particular (yet common) casewhere the density is computed exactly at the locations of the data pointsrather than at an uncorrelated set of locations. By default, the algorithmcombines a top-hat kernel with M0=2.0 with the balloon estimator and appliesthe corresponding bias correction. These settings are shown to yield reasonableresults for a simple test case, a two-dimensional ring, that illustrates theperformance for oblique distributions, as well as for a six-dimensionalHernquist sphere, a fairly realistic model of the dynamical structure ofstellar bulges in galaxies and dark matter haloes in cosmological N-bodysimulations. Results for different parameter settings are discussed in order toprovide a guideline to select an optimal configuration in other cases. Sourcecode is available upon request.

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