Simultaneous estimation of noise variance and number of peaks in Bayesian spectral deconvolution

Heuristic identification of peaks from noisy complex spectra often leads to misunderstanding physical and chemical properties of matter. In this paper, we propose a framework based on Bayesian inference, which enables us to separate multi-peak spectra into single peaks statistically and is constructed in two steps. The first step is estimating both noise variance and number of peaks as hyperparameters based on Bayes free energy, which generally is not analytically tractable. The second step is fitting the parameters of each peak function to the given spectrum by calculating the posterior density, which has a problem of local minima and saddles since multi-peak models are nonlinear and hierarchical. Our framework enables escaping from local minima or saddles by using the exchange Monte Carlo method and calculates Bayes free energy. We discuss a simulation demonstrating how efficient our framework is and show that estimating both noise variance and number of peaks prevents overfitting, overpenalizing, and misunderstanding the precision of parameter estimation.