Bayesian Inference for Small-Angle Scattering Data II: Core-Shell Samples

TL;DR

This paper develops a Bayesian inference method for analyzing small-angle scattering data using a complex core-shell model, demonstrating its effectiveness and conditions for accurate parameter estimation.

Contribution

It introduces a Bayesian analytical approach for the more complex core-shell model in SAS data analysis, extending previous sphere model methods.

Findings

Effective parameter estimation under various measurement conditions

Identified conditions for accurate core-shell model analysis

Validated method through numerical experiments

Abstract

Small-angle scattering (SAS) techniques, which utilize neutrons and X-rays, are employed in various scientific fields, including materials science, biochemistry, and polymer physics. During the analysis of SAS data, model parameters that contain information about the sample are estimated by fitting the observational data to a model of sample. Previous research has demonstrated the effectiveness of Bayesian inference in analyzing SAS data using a sphere model. However, compared with the sphere model, the core-shell model, which represents functional nanoparticles, offers higher application potential and greater analytical value. Therefore, in this study, we propose an analytical method for the more complex and practical core-shell model based on Bayesian inference. Through numerical experiments, we evaluated the performance of this method under different conditions, including measurement times, number of data points, and differences in scattering length density. As a result, we clarify the conditions under which accurate estimations are possible.