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Identifying a peptide on the basis of a scan from a mass spectrometer is an important yet highly challenging problem. To identify peptides, we present a Bayesian approach which uses prior information about the average relative abundances of bond cleavages and the prior probability of any particular amino acid sequence. The scoring function proposed is composed of two overall distance measures, which measure how close an observed spectrum is to a theoretical scan for a peptide. Our use of our scoring function, which approximates a likelihood, has connections to the generalization presented by Bissiri and co-workers of the Bayesian framework. A Markov chain Monte Carlo algorithm is employed to simulate candidate choices from the posterior distribution of the peptide sequence. The true peptide is estimated as the peptide with the largest posterior density.