Mechanistic models informed by lower-length-scale simulations have a role to play in accelerating fuel qualification by enabling the use of separate effects tests to reduce uncertainty on model parameters that impact the predictions of in-reactor performance. For this to succeed, statistical analysis techniques (e.g. Bayesian inference) must be exercised on the mechanistic models to determine parameter uncertainties that are based on evidence (experiments). Here, we employ Bayesian inference on an atomic-scale-informed model for UO2 creep using literature experimental data. Pellet creep plays a significant role in pellet-cladding mechanical interactions, which affect fuel performance. The objective is to infer probability distributions on the atomic-scale parameters used in the model, while accounting for experimental uncertainties and unknowns. The approach requires many evaluations of the model, which becomes computationally insurmountable; therefore, a neural network model is trained to data obtained by sampling the full model over the most important parameters. This machine-learning model is then used in the Bayesian inference approach to determine probability distributions in the parameter values that represent the uncertainty in the model given what is known from the experiments (posterior). A significant reduction compared to conservative initial (prior) uncertainties is achieved through inference against the experimental data, demonstrating the efficacy of this approach. Furthermore, by accounting for uncertainties in the experimental conditions and sample nonstoichiometry, it is possible to resolve apparent discrepancies in experimental measurements within a self-consistent grain boundary (Coble) creep model that is sensitive to chemistry.