EnBiD: Fast Multidimensional Density Estimation
Abstract
We present a method to numerically estimate the densities of a discretely sampled data based on a binary space partitioning tree. We start with a root node containing all the particles and then recursively divide each node into two nodes each containing roughly equal number of particles, until each of the nodes contains only one particle. The volume of such a leaf node provides an estimate of the local density and its shape provides an estimate of the variance. We implement an entropybased node splitting criterion that results in a significant improvement in the estimation of densities compared to earlier work. The method is completely metric free and can be applied to arbitrary number of dimensions. We use this method to determine the appropriate metric at each point in space and then use kernelbased methods for calculating the density. The kernelsmoothed estimates were found to be more accurate and have lower dispersion. We apply this method to determine the phasespace densities of dark matter haloes obtained from cosmological Nbody simulations. We find that contrary to earlier studies, the volume distribution function v(f) of phasespace density f does not have a constant slope but rather a small hump at high phasespace densities. We demonstrate that a model in which a halo is made up by a superposition of Hernquist spheres is not capable in explaining the shape of v(f) versus f relation, whereas a model which takes into account the contribution of the main halo separately roughly reproduces the behaviour as seen in simulations. The use of the presented method is not limited to calculation of phasespace densities, but can be used as a general purpose datamining tool and due to its speed and accuracy it is ideally suited for analysis of large multidimensional data sets.
 Publication:

Astrophysics Source Code Library
 Pub Date:
 September 2011
 Bibcode:
 2011ascl.soft09012S
 Keywords:

 Software