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：本文提出一种基于贝叶斯推断框架、利用小角散射（SAS）数据估计模型参数的方法。传统SAS数据分析涉及分析人员手动调整参数或使用梯度法进行优化的过程。这类分析往往采用启发式方法，容易陷入局部最优解。此外，传统分析方法难以评估结果的可靠性。我们的方法通过贝叶斯推断框架，将模型参数从SAS数据中估计为概率分布，从而解决了上述问题。我们使用代表性测量目标模型的人工数据，通过数值实验评估了该方法性能。数值实验结果表明，该方法不仅具有高精度和高可靠性，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。