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 1
Schematic representation of the reduced error surface $[\widehat{{\cal E}}(\widehat{h},\rho)]$ as a function of the normalized bin width $[\widehat{h}]$ and the degree of smoothing $[\rho = h/\lambda]$ . The total error decomposes into three additive components: counting error $[G(\rho)/\widehat{h}]$ (red), aliasing bias $[\widehat{h}^{2}]$ (blue) and curvature correction $[\widehat{h}^{4}[M_{2}(\rho)]^{2}]$ (green). The red arrow on the 3D surface indicates the direction of decreasing total error as stronger smoothing (smaller ρ) is applied, highlighting the transition from the uncorrelated FD regime ( $[\rho\ \gt\ 1]$ ) to the correlation-dominated GP regime ( $[\rho\ \lt\ 1]$ ).

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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