Abstract Climate change impact studies are subject to numerous uncertainties and assumptions. One of the main sources of uncertainty arises from the interpretation of climate model projections. Probabilistic procedures based on multimodel ensembles have been suggested in the literature to quantify this source of uncertainty. However, the interpretation of multimodel ensembles remains challenging. Several assumptions are often required in the uncertainty quantification of climate model projections. For example, most methods often assume that the climate models are independent and/or that changes in climate model biases are negligible. This study develops a Bayesian framework that accounts for model dependencies and changes in model biases and compares it to estimates calculated based on a frequentist approach. The Bayesian framework is used to investigate the effects of the two assumptions on the uncertainty quantification of extreme precipitation projections over Denmark. An ensemble of regional climate models from the Ensemble-Based Predictions of Climate Changes and their Impacts (ENSEMBLES) project is used for this purpose. The results confirm that the climate models cannot be considered independent and show that the bias depends on the value of precipitation. This has an influence on the results of the uncertainty quantification. Both the mean and spread of the change in extreme precipitation depends on both assumptions. If the models are assumed independent and the bias constant, the results will be overconfident and may be treated as more precise than they really are. This study highlights the importance of investigating the underlying assumptions in climate change impact studies, as these may have serious consequences for the design of climate change adaptation strategies.