Model Design in Bayesian Spectral Deconvolution

Abstract

Bayesian spectral deconvolution is a powerful tool for analyzing complex spectra with overlapping peaks. It can not only decompose the overlapping peaks and estimate parameters such as the position, height, and width of each peak, but also estimate the number of included peaks from the spectral data themselves through Bayesian model selection. To estimate the number of peaks, we prepare models with different numbers of peaks for a given spectrum, and calculate the evidence for these models. The number of peaks in the model with the highest evidence is adopted as an estimate of the number of peaks in the given spectrum. However, when the difference in evidence between models with different numbers of peaks is small, low-precision estimates of the evidence lead to a high error probability in the peak number estimation. In this study, we propose an appropriate model design that will increase the difference in evidence between different peak number models. This allows us to reduce the error probability even with low-precision estimates.