In this paper, we propose a method for estimating model parameters using Small-Angle Scattering (SAS) data based on the Bayesian inference. Conventional SAS data analyses involve processes of manual parameter adjustment by analysts or optimization using gradient methods. These analysis processes tend to involve heuristic approaches and may lead to local solutions.Furthermore, it is difficult to evaluate the reliability of the results obtained by conventional analysis methods. Our method solves these problems by estimating model parameters as probability distributions from SAS data using the framework of the Bayesian inference. We evaluate the performance of our method through numerical experiments using artificial data of representative measurement target models.From the results of the numerical experiments, we show that our method provides not only high accuracy and reliability of estimation, but also perspectives on the transition point of estimability with respect to the measurement time and the lower bound of the angular domain of the measured data.

翻译：本文提出了一种基于贝叶斯推断框架、利用小角散射数据估计模型参数的方法。传统小角散射数据分析通常依赖分析人员手动调节参数或使用梯度方法进行优化，这些分析过程往往涉及启发式方法，且可能陷入局部最优解。此外，传统分析方法难以评估所得结果的可靠性。我们的方法通过采用贝叶斯推断框架，将模型参数从散射数据中估计为概率分布形式，从而解决了上述问题。我们利用代表性测量目标模型的人工数据进行数值实验，以评估所提方法的性能。数值实验结果表明，该方法不仅能够提供高精度和高可靠性的估计，还能揭示测量时间与测量数据角域下限对参数可估性转变点的影响。