We present an analysis which suggests that model selection is a critical ingredient for successful reconstruction of impurity transport coefficient profiles, D and V, from experimental data. Determining these quantities is a challenging nonlinear inverse problem. We use synthetic data to show that this problem is ill-posed, and hence D and V are not recommended for use in validation metrics unless the data analysis procedure goes to great lengths to account for the possibility that there are multiple possible solutions. In particular, inferred profiles which are very different from the true ones yield seemingly reasonable goodness-of-fit for synthetic x-ray spectrometer data. We present a Bayesian approach for inferring D and V which provides a rigorous means of selecting the level of complexity of the inferred profiles, thereby enabling successful reconstruction of the profiles.