Optimization and inference of bin widths for histogramming inelastic neutron scattering spectra

A data-driven bin-width optimization for the histograms of measured data sets based on inhomogeneous Poisson processes was developed in a neurophysiology study [Shimazaki & Shinomoto (2007). Neural Comput. 19, 1503-1527], and a subsequent study [Muto, Sakamoto, Matsuura, Arima & Okada (2019). J. Phys. Soc. Jpn, 88, 044002] proposed its application to inelastic neutron scattering (INS) data. In the present study, the results of the method on experimental INS time-of-flight data collected under different measurement conditions from a copper single crystal are validated. The extrapolation of the statistics on a given data set to other data sets with different total counts precisely infers the optimal bin widths on the latter. The histograms with the optimized bin widths statistically verify two fine-spectral-feature examples in the energy and momentum transfer cross sections: (i) the existence of phonon band gaps; and (ii) the number of plural phonon branches located close to each other. This indicates that the applied method helps in the efficient and rigorous observation of spectral structures important in physics and materials science like novel forms of magnetic excitation and phonon states correlated to thermal conductivities.