Bayesian Inference for Small-Angle Scattering Data

In this paper, we propose a method of 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 generated using representative measurement target models. From the results of numerical experiments, we show that our method provides not only highly accurate and reliable estimations, but also perspectives on the transition point of estimability with respect to the measurement time and the lower bound of the angular region of the measured data.