Analysis of astrophysical spectra places a great emphasis on statistical tools to ensure that the models being applied best fit the data which are observed. There are increasing efforts to model telescopes and instruments in ever more intensive ways to allow for uncertainties in the calibration and their subsequent effects on the spectra. However, while the spectroscopic diagnostics which can be extracted from these spectral are widely used powerful tools for identifying both the plasma state and composition, the contribution of uncertainties on the fundamental atomic data to such diagnostics has not been well understood. Work is described that outlines a method for assigning uncertainties on fundamental atomic structure and collision data, that can then be propagated through to uncertainties on spectroscopic diagnostics and plasma modeling codes. Structural uncertainties are inferred from available data by means of Bayesian analysis and their underlying distributions are interrogated through Markov chain Monte-Carlo sampling. The approach is designed to be general in nature and can be applied to a range of atomic processes, with examples given for dielectronic recombination and electron-impact excitation.