Many methods have previously been devised to estimate the relative amounts of chemicals present in a measured Raman spectrum. However, relatively little work has been done on developing physics-based probabilistic models for the measurement system. Drawing from previous work in astronomical image restoration, we model the acquired data based on the physics of two key components in our Raman instrumentation: the spectrometer and the charge-coupled device detector. Under this model, we derive Cramér-Rao lower bounds for the mixing coefficients of the target spectra. This bound is compared against the performance of several classification algorithms. The non-negative iteratively reweighted least-squares algorithm is seen to give performance that is nearly identical to the more computationally demanding expectation-maximization approach; this is true even at weak signal levels.