Kernel density estimation of a multidimensional efficiency profile

TL;DR

This paper proposes a correction method for kernel density estimation to better describe narrow structures and boundaries, especially useful for analyzing multidimensional efficiency profiles in particle physics.

Contribution

It introduces an approach that uses an approximate density to improve kernel density estimates for narrow features and boundaries in multidimensional data.

Findings

Effective correction for boundary effects in kernel density estimation.

Improved description of efficiency shapes in multidimensional phase space.

Application demonstrated on five-dimensional decay data.

Abstract

Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data samples, whereas if the kernel width is large, boundaries and narrow structures tend to be smeared. Here, an approach to correct for such effects, is proposed that uses an approximate density to describe narrow structures and boundaries. The approach is shown to be well suited for the description of the efficiency shape over a multidimensional phase space in a typical particle physics analysis. An example is given for the five-dimensional phase space of the $\Lambda_b^0\to D^0p\pi$ decay.