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 2
(a) Reduced error surface $[\widehat{{\cal E}}(\widehat{h},\rho)]$ showing that the minimum-error locus (red line) bends toward smaller normalized bin width $[\widehat{h}]$ as the degree of smoothing increases (smaller ρ). The FD rule serves as a boundary separating distinct behaviors in the GP-smoothed results. (b) and (c) Cross-sections of the surface at fixed $[\widehat{h} = 0.1\,\widehat{h}_{{\rm opt}}^{{\rm FD}}]$ and $[\widehat{h} = 3\,\widehat{h}_{{\rm opt}}^{{\rm FD}}]$ , respectively. When the bin width is smaller than the FD optimum, a well-defined minimum below the nominal FD result emerges for an appropriate kernel length, marked by the black circle in (b). For larger bins, additional smoothing no longer improves accuracy, as the aliasing and curvature terms dominate, as shown in panel (c).

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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