Bayesian free-energy model selection for amide I band decomposition in multiplex coherent anti-Stokes Raman scattering (CARS) microscopy

Traditional amide I spectral decomposition requires prior specification of component number and initial parameters from previous studies. Here, we apply Bayesian free-energy model selection to compare Gaussian models with different numbers of components for a coherent anti-Stokes Raman scattering (CARS)-derived spontaneous-Raman-equivalent Im[χ(3)] spectrum. When applied to the amide I spectrum of a drug-treated binucleated human mammary epithelial cell (HMEC), the four-component model showed the lowest Bayesian free energy and the highest posterior model probability of 72.4% among the tested candidate models. In a separate dataset from an untreated mononucleated HMEC, Bayesian free energy exhibited internal minima at K = 3 for the amide I region and K = 6 for the CH stretching region, whereas RSS decreased monotonically with increasing model complexity in both cases. This workflow reduces user-dependent bias and improves the reproducibility of spectral decomposition in single-cell CARS analysis when the likelihood, prior ranges, candidate models, and preprocessing procedures are explicitly specified.