Multidimensional Bin-Width Optimization For Histogram And Its Application To Four-Dimensional Neutron Inelastic Scattering Data

We propose a method for optimizing bin widths for multidimensional histograms. The optimization criterion is based on a cost function representing the tradeoff between the reduction of stochastic fluctuation and extraction of the structure that the data have. In recent years, a large amount of four-dimensional event data have been obtainable in neutron inelastic scattering experiments conducted by chopper spectrometers at Japan Proton Accelerator Research Complex (J-PARC). As preprocessing, researchers make histograms from obtained event data. At present, the researchers only empirically select bin widths and slice conditions to obtain a two-dimensional histogram, while checking the histogram in a visual approach. We propose a method that can automatically make a multidimensional histogram from event data. In this paper, we use artificial data to investigate the behavior of our method. The artificial four-dimensional event data were produced, assuming neutron inelastic scattering due to phonons. We applied the proposed method to both sliced two-dimensional event data and the whole four-dimensional event data. Comparing their results, we have found that the optimized bin widths strongly depends on the dimensionality of the data. Moreover, the optimal bin widths are affected by the number of events and the magnitude of the white background noise.