Optimal Binning for Small-Angle Neutron Scattering Data Using the Freedman-Diaconis Rule
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914117500010496 |
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| author | An, Jessie E. Tung, Chi-Huan Do, Changwoo Chen, Wei-Ren |
| author_facet | An, Jessie E. Tung, Chi-Huan Do, Changwoo Chen, Wei-Ren |
| contents | Small-Angle Neutron Scattering (SANS) data analysis often relies on fixed-width binning schemes that overlook variations in signal strength and structural complexity. We introduce a statistically grounded approach based on the Freedman-Diaconis (FD) rule, which minimizes the mean integrated squared error between the histogram estimate and the true intensity distribution. By deriving the competing scaling relations for counting noise ($\propto h^{-1}$) and binning distortion ($\propto h^{2}$), we establish an optimal bin width that balances statistical precision and structural resolution. Application to synthetic data from the Debye scattering function of a Gaussian polymer chain demonstrates that the FD criterion quantitatively determines the most efficient binning, faithfully reproducing the curvature of $I(Q)$ while minimizing random error. The optimal width follows the expected scaling $h_{\mathrm{opt}} \propto N_{\mathrm{total}}^{-1/3}$, delineating the transition between noise- and resolution-limited regimes. This framework provides a unified, physics-informed basis for adaptive, statistically efficient binning in neutron scattering experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Binning for Small-Angle Neutron Scattering Data Using the Freedman-Diaconis Rule An, Jessie E. Tung, Chi-Huan Do, Changwoo Chen, Wei-Ren Data Analysis, Statistics and Probability Applied Physics Instrumentation and Detectors Small-Angle Neutron Scattering (SANS) data analysis often relies on fixed-width binning schemes that overlook variations in signal strength and structural complexity. We introduce a statistically grounded approach based on the Freedman-Diaconis (FD) rule, which minimizes the mean integrated squared error between the histogram estimate and the true intensity distribution. By deriving the competing scaling relations for counting noise ($\propto h^{-1}$) and binning distortion ($\propto h^{2}$), we establish an optimal bin width that balances statistical precision and structural resolution. Application to synthetic data from the Debye scattering function of a Gaussian polymer chain demonstrates that the FD criterion quantitatively determines the most efficient binning, faithfully reproducing the curvature of $I(Q)$ while minimizing random error. The optimal width follows the expected scaling $h_{\mathrm{opt}} \propto N_{\mathrm{total}}^{-1/3}$, delineating the transition between noise- and resolution-limited regimes. This framework provides a unified, physics-informed basis for adaptive, statistically efficient binning in neutron scattering experiments. |
| title | Optimal Binning for Small-Angle Neutron Scattering Data Using the Freedman-Diaconis Rule |
| topic | Data Analysis, Statistics and Probability Applied Physics Instrumentation and Detectors |
| url | https://arxiv.org/abs/2510.09581 |