Bayesian Inference of Absorption Spectra Based on Binomial Distribution

Abstract: In this paper, we propose a Bayesian spectral deconvolution method for absorption spectra. In conventional analysis, the noise mechanism of absorption spectral data is never considered appropriately. In that analysis, the least-squares method, which assumes Gaussian noise from the perspective of Bayesian statistics, is frequently used. Since Bayesian inference is possible by introducing an appropriate noise model for the data, we consider the absorption process of a single photon to be a Bernoulli trial and develop a Bayesian spectral deconvolution method based on binomial distribution. We have evaluated our method on artificial data under several conditions by numerical experiments. The results show that our method not only allows us to estimate parameters with high accuracy from absorption spectral data, but also to infer them even from absorption spectral data with large absorption rates where the spectral structure is flattened, which was previously impossible to analyze.