A Kernel Density Approach to Multidimensional Neutrinoless Double Beta Decay Fits in SNO+

Analysis of SNO+ data typically involves a maximum likelihood fit of many backgrounds and signal event classes represented by multidimensional probability density functions (PDFs). However, binned histograms, which are typically used for estimating PDFs, require an impractical amount of Monte-Carlo (MC) statistics in higher dimensions to achieve an accurate PDF estimate. Position within the detector and the reconstructed energy of an interaction are important dimensions in these PDFs, and classification scores based on additional information, such as topology, can be included to improve discrimination of signal and background events. Kernel density estimation (KDE) with adaptive bandwidth can be used to provide an accurate estimate of such PDFs with fewer MC statistics than binned histograms require. This approach also provides a convenient method for including systematic uncertainties in the maximum likelihood fit. Here, a framework for using KDE accelerated on GPUs is explored as a technique for analyzing neutrinoless double beta decay data with multidimensional PDFs.