DPA estimates the probability associated with the ensemble of configurations projected in a given point i of the configuration space S, using the PAk density esitmator , based on the Euclidean distances between point i and its k nearest neighbors. An underpinning assumption of this method is that the density is constant in the neighborhood of the point i. Hence, the parameter k is selected to be as large as possible to maximize the data used in calculating the local density while still representing a hypervolume of constant density. Each neighbor l can be said to occupy the volume v l of the hyperspherical shell enclosed between hyperspheres of radii r l and r l-1 . The sum of these volumes up to neighbor k is equal to volume V k of a hypersphere with radius r k . DPA leverages the fact that for a region of constant density, the volumes will be drawn from an exponential distribution with a rate of this density ρ and that thus the log-likelihood function of ρ given a set of k neighbors is given by