  We propose a Bayesian statistical model for analyzing coherent anti-Stokes
Raman scattering (CARS) spectra. Our quantitative analysis includes statistical
estimation of constituent line-shape parameters, underlying Raman signal,
error-corrected CARS spectrum, and the measured CARS spectrum. As such, this
work enables extensive uncertainty quantification in the context of CARS
spectroscopy. Furthermore, we present an unsupervised method for improving
spectral resolution of Raman-like spectra requiring little to no \textit{a
priori} information. Finally, the recently-proposed wavelet prism method for
correcting the experimental artefacts in CARS is enhanced by using
interpolation techniques for wavelets. The method is validated using CARS
spectra of adenosine mono-, di-, and triphosphate in water, as well as,
equimolar aqueous solutions of D-fructose, D-glucose, and their disaccharide
combination sucrose.
