Bayesian parameter estimation from dispersion relation observation data with Poisson process

In this study, we estimate the distribution of lattice model parameters based on Bayesian estimation using the dispersion relation spectral data of lattice vibration. The dispersion relation of lattice vibration is observed using inelastic scattering of neutrons or x rays and is used to analyze the speed of sound and interatomic force. However, the current analysis method of dispersion relation observation data in the field of experimental physics requires manually fitting parameters, so the analysis is costly and cannot effectively handle high-dimensional data and large amounts of data. Moreover, it is impossible to discuss the estimation accuracy with the conventional method. Therefore, we solve these problems by estimating the distribution of parameters using Bayesian inference. We propose a lattice model parameter estimation method that uses Bayesian inference with a physical observation stochastic process and determine the method's effectiveness using artificial data.