Correlation-aware binning for small-angle neutron scattering via Gaussian-process inference

Tung, C.-H.; Do, C.; Jang, J.; Lee, S.; Huang, G.-R.; Porcar, L.; Wang, Y.; Shinohara, Y.; Chen, W.-R.

doi:10.1107/S1600576726000907

Journal of Applied Crystallography Journal of Applied
Crystallography

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Figure 4
Evaluation of the optimal bin width and error scaling as a function of total detector counts n. (a) Comparison between the Freedman–Diaconis bin width $[h_{{\rm FD}}]$ (black circles) and the instrument-limited pixel size $[h_{{\rm instr}}]$ (red line) for the PEG-b-PLAyne-b-PLA triblock copolymer solution measured at HANARO. A crossover near $[n\simeq 3\times 10^{5}]$ marks the transition where $[h_{{\rm FD}}]$ approaches the instrumental resolution. The inset shows the measured I(Q) for the shortest ( $[n = 10^{4}]$ ) and longest ( $[n = 2\times 10^{7}]$ ) acquisitions. (b) Mean-squared error $[{\cal E}]$ obtained from data binned at $[h_{{\rm instr}}]$ (red), at the FD optimum (black) and after GP refinement (blue). Dashed lines indicate $[n^{-1}]$ and $[n^{-4/5}]$ scaling, and the shaded region marks the theoretical lower bound. (c) Relative improvement $[{\cal E}/{\cal E}_{{\rm instr}}]$ , showing that GP postprocessing (blue) further reduces the mean-squared error compared with direct binning (red) and the FD-optimized result (black).

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 59| Part 2| April 2026| Pages 334-342

https://doi.org/10.1107/S1600576726000907

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