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 3
Convergence of the parameters α, β and γ and their impact on the estimation of $[h_{{\rm FD}}]$ and $[\lambda_{{\rm opt}}]$ . (a)–(c) Evolution of α, β and γ as functions of total detector counts n, evaluated using the Savitzky–Golay method (Press et al., 2007

) for numerical differentiation. The shaded regions indicate the associated uncertainties. (d) Corresponding estimates of the optimal Freedman–Diaconis bin width $[h_{{\rm FD}}]$ (black circles) and the GP kernel length $[\lambda_{{\rm opt}}]$ (blue squares) as functions of n. The inset in panel (a) shows the measured scattering intensity I(Q) obtained from the phospholipid and hyaluronan aggregate solution used for convergence testing, comparing the shortest ( $[n = 10^{3}]$ ) and longest ( $[n = 3\times 10^{6}]$ ) measurements included in this analysis. The consistent evolution of the parameters with increasing n confirms the robustness of the estimation procedure and the stability of the derived statistical coefficients.

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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