Bayesian Parameter Estimation Using Dispersion Relation Spectra

In this paper, we propose a method for estimating the physical parameters from dispersion relation data. The conventional analysis method for dispersion relation data has a process of fitting parameters manually, so the analysis cost is high and the method cannot handle large amounts of data or high-dimensional data effectively. Moreover, it is impossible to discuss the estimation confidence with the conventional method. Therefore, we estimate the parameter distribution using Bayesian inference to solve these problems. In this paper, we propose two estimation methods. One is an indirect method that estimates the dispersion relation from spectral data and estimates physical parameters from it. The other is a direct method that estimates physical parameters directly from spectral data. We evaluated the performance of both methods using synthetic data. In addition, we show that the bias of the amount of information by estimation using random sampling data in the momentum space and discuss efficient sampling.