Information about the physical properties of astrophysical objects cannot be measured directly but is inferred by interpreting spectroscopic observations in the context of atomic physics calculations. Ratios of emission lines, for example, can be used to infer the electron density of the emitting plasma. Similarly, the relative intensities of emission lines formed over a wide range of temperatures yield information on the temperature structure. A critical component of this analysis is understanding how uncertainties in the underlying atomic physics propagate to the uncertainties in the inferred plasma parameters. At present, however, atomic physics databases do not include uncertainties on the atomic parameters and there is no established methodology for using them even if they did. In this paper we develop simple models for uncertainties in the collision strengths and decay rates for Fe xiii and apply them to the interpretation of density-sensitive lines observed with the EUV (extreme ultraviolet) Imagining spectrometer (EIS) on Hinode. We incorporate these uncertainties in a Bayesian framework. We consider both a pragmatic Bayesian method where the atomic physics information is unaffected by the observed data, and a fully Bayesian method where the data can be used to probe the physics. The former generally increases the uncertainty in the inferred density by about a factor of 5 compared with models that incorporate only statistical uncertainties. The latter reduces the uncertainties on the inferred densities, but identifies areas of possible systematic problems with either the atomic physics or the observed intensities.