Recent advances in the development of technology based on Raman scattering as a chemical analytical technique have made it possible to quantitatively detect spectral mixtures of multiple DNA sequences. However, to fully exploit these techniques inferential methodologies are required which can deconvolute the observed mixture and infer the composition of distinct DNA sequences present in the overall composite. Inferring the spectral decomposition is posed as a model selection problem for a bilinear statistical model, and the required Markov chain Monte Carlo inferential methodology is developed. In particular a Gibbs sampler and Reversible Jump Markov chain Monte Carlo methods are presented along with techniques based on estimation of the marginal likelihood. The results reported in this paper are particularly encouraging highlighting that for multiplexed Raman spectra, inference of the composition of original sequences present in the mixture is possible to acceptable levels of accuracy. This statistical methodology makes the exploitation of multiplexed surface enhanced resonance Raman scattering spectra in disease identification a reality.