小角中子散射数据的最优分箱：基于Freedman-Diaconis规则
Optimal Binning for Small-Angle Neutron Scattering Data Using the Freedman-Diaconis Rule
AI总结：
本文提出基于Freedman-Diaconis规则的最优分箱方法，用于小角中子散射数据，平衡统计精度与结构分辨率，并在合成数据上验证了其有效性。
摘要：
小角中子散射（SANS）数据分析通常依赖于固定宽度的分箱方案，这些方案忽视了信号强度和结构复杂性的变化。我们引入了一种基于Freedman-Diaconis（FD）规则的统计方法，该方法最小化直方图估计与真实强度分布之间的平均积分平方误差。通过推导计数噪声（$\propto h^{-1}$）和分箱失真（$\propto h^{2}$）的竞争标度关系，我们建立了平衡统计精度和结构分辨率的最优箱宽。对高斯聚合物链的Debye散射函数合成数据的应用表明，FD准则定量地确定了最高效的分箱方式，在忠实再现$I(Q)$曲率的同时最小化随机误差。最优宽度遵循预期标度$h_{\mathrm{opt}} \propto N_{\mathrm{total}}^{-1/3}$，描绘了噪声受限与分辨率受限区域之间的转变。该框架为中子散射实验中自适应、统计高效的分箱提供了统一且基于物理的基准。
英文摘要：
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.
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