Development of spectral decomposition based on Bayesian information criterion with estimation of confidence interval

We develop an automatic peak fitting algorithm using the Bayesian information criterion (BIC) fitting method with confidence-interval estimation in spectral decomposition. First, spectral decomposition is carried out by adopting the Bayesian exchange Monte Carlo method for various artificial spectral data, and the confidence interval of fitting parameters is evaluated. From the results, an approximated model formula that expresses the confidence interval of parameters and the relationship between the peak-to-peak distance and the signal-to-noise ratio is derived. Next, for real spectral data, we compare the confidence interval of each peak parameter obtained using the Bayesian exchange Monte Carlo method with the confidence interval obtained from the BIC-fitting with the model selection function and the proposed approximated formula. We thus confirm that the parameter confidence intervals obtained using the two methods agree well. It is therefore possible to not only simply estimate the appropriate number of peaks by BIC-fitting but also obtain the confidence interval of fitting parameters.