论文标题
可以使用贝叶斯间接傅立叶变换来评估小角度散射中的实验噪声
Experimental noise in small-angle scattering can be assessed using the Bayesian indirect Fourier transformation
论文作者
论文摘要
小角度X射线和中子散射被广泛用于研究软物质和生物物理系统。在评估假设模型对数据的拟合程度时，实验误差至关重要。同样，当将权重分配给用于完善相同模型的多个数据集时，它们也很重要。因此，当实验错误被过度估计时，这是有问题的。提出了一种方法，使用贝叶斯间接傅立叶转化用于小角度散射数据，以评估给定的小角度散射数据集是否具有过度估计或估计的实验错误。该方法对模拟数据和实验数据都是有效的，可用于相应地评估和重新列出错误。即使估计的实验错误是适当的，模型是否符合足够符合的模型，因为“ true”减少了数据的$χ^2 $不一定是统一性。这与过度拟合是固有挑战的方法尤其重要，例如，针对小角度散射数据或从头算建模重新加权分子动力学轨迹。使用概述的方法，可以证明人们可以在将模型与小角度散射数据拟合时确定$χ^2 $的目标。该方法可以通过Web接口贝内斯普轻松访问。
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 under-estimated. 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 under-estimated 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 $χ^2$ 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 $χ^2$ to aim for when fitting a model against small-angle scattering data. The method is easily accessible via the web interface BayesApp.
