Rutherford backscattering spectrometry has been used to obtain quantitative and traceable information about homogeneous films. However, inhomogeneous films cannot be analysed with the same manual calculation methods. We have previously demonstrated that a machine algorithm using simulated annealing is available to extract depth profiles from spectra obtained from such inhomogeneous samples. In this work we show how a Bayesian error analysis can be used to construct error bounds on these depth profiles reflecting the uncertainty introduced by Poisson noise on the data. Hence we present, for the first time. RES analysis which not only gives fully quantitative depth profiles for complex samples, but also reliable estimates of the errors due to collection statistics on these profiles.