In this paper we develop a method for the decomposition of mass spectra of gas mixtures, together with the relevant calibration measurements. The method is based on Bayesian probability theory. Given a set of spectra, the algorithm returns the relative concentrations and the associated margin of confidence for each component of the mixture. In addition to the concentrations, such a data set enables the derivation of improved values of the cracking coefficients of all contributing species, even for those components for which the set does not contain a calibration measurement. This latter feature also allows one to analyze mixtures that contain radicals in addition to stable molecules. As an example, we analyze and discuss the mass spectra obtained from the pyrolysis of azomethane, which contain the radical CH3 apart from nitrogen and C1- and C2-hydrocarbons.