Smoothed multi-variate histogrammed PDEs, and χ2χ2 optimisation

With increasing requirements from particle physics for effective multi-variate discrimination techniques, a number of alternative probability density estimate (PDE) methods have appeared in recent years. These relatively advanced methods attempt to form effective PDEs in the presence of low statistics where a simple histogramming method does not perform well.In this paper a multi-variate histogrammed PDE method is presented. The method incorporates a simple Laplace smoothing procedure and χ2χ2-triggered optimisation that results in the automatic selection of near-optimal binning and greatly improved PDE performance at low statistics.The performance of the smoothed histogrammed PDE is compared to a theoretically ideal PDE, and to results from a kernel PDE and a neural network.