Raman spectroscopy can be used to identify molecules by the characteristic scattering of light from a laser. Each Raman-active dye label has a unique spectral signature, comprised by the locations and amplitudes of the peaks. We represent these spectra using a generalised additive mixed model (GAMM). The Raman peaks are modelled using Lorentzian kernels, while the background fluorescence is estimated using a penalised spline. The amplitudes of the peaks are completely dependent on the position of the baseline and vice-versa. Errors in baseline correction can make it difficult to identify and quantify the dyes, particularly when several dyes are present in a multiplexed spectrum. We introduce a sequential Monte Carlo algorithm for joint estimation of the baseline and peaks. Our model-based approach accounts for differences in resolution and experimental conditions, enabling comparison and alignment of heterogeneous spectra. By incorporating this representation into a hierarchical regression, we can quantify the relationship between dye concentration and peak intensity and provide an improved estimate of the limit of detection. This is joint work with Mark Girolami and Jake Carson at the University of Warwick and Kirsten Gracie, Karen Faulds, and Duncan Graham at the University of Strathclyde.