Small-angle X-ray and neutron scattering are widely used to investigate soft matter and biophysical systems. The experimental errors are essential when assessing how well a hypothesized model fits the data. Likewise, they are important when weights are assigned to multiple data sets used to refine the same model. Therefore, it is problematic when experimental errors are over- or underestimated. A method is presented, using Bayesian indirect Fourier transformation for small-angle scattering data, to assess whether or not a given small-angle scattering data set has over- or underestimated experimental errors. The method is effective on both simulated and experimental data, and can be used to assess and rescale the errors accordingly. Even if the estimated experimental errors are appropriate, it is ambiguous whether or not a model fits sufficiently well, as the `true' reduced χ² of the data is not necessarily unity. This is particularly relevant for approaches where overfitting is an inherent challenge, such as reweighting of a simulated molecular dynamics trajectory against small-angle scattering data or ab initio modelling. Using the outlined method, it is shown that one can determine what reduced χ² to aim for when fitting a model against small-angle scattering data. The method is easily accessible via the web interface BayesApp.

中文翻译：

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可以使用贝叶斯间接傅里叶变换评估小角度散射中的实验噪声

小角度 X 射线和中子散射广泛用于研究软物质和生物物理系统。在评估假设模型与数据的拟合程度时，实验误差是必不可少的。同样，当权重分配给用于优化同一模型的多个数据集时，它们很重要。因此，当实验误差被高估或低估时，就会出现问题。提出了一种方法，对小角度散射数据使用贝叶斯间接傅里叶变换，以评估给定的小角度散射数据集是否具有高估或低估的实验误差。该方法对模拟和实验数据均有效，可用于评估和相应地重新调整误差。即使估计的实验误差是合适的，²的数据不一定是统一的。这对于过度拟合是固有挑战的方法尤其相关，例如根据小角度散射数据或从头建模重新加权模拟分子动力学轨迹。使用概述的方法，可以确定在针对小角度散射数据拟合模型时，可以确定减少的 χ ²的目标。该方法可通过 Web 界面BayesApp轻松访问。