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Research on uncertainty quantification and mitigation of software-intensive systems and (self-)adaptive systems, is increasingly gaining momentum, especially with the availability of statistical inference techniques (such as Bayesian reasoning) that make it possible to mitigate uncertain (quality) attributes of the system under scrutiny often encoded in the system model in terms of model parameters. However, to the best of our knowledge, the uncertainty about the choice of a specific system model did not receive the deserved attention. This paper focuses on self-adaptive systems and investigates how to mitigate the uncertainty related to the model selection process, that is, whenever one model is chosen over plausible alternative and competing models to represent the understanding of a system and make predictions about future observations. In particular, we propose to enhance the classical feedback loop of a self-adaptive system with the ability to tame the model uncertainty using Bayesian Model Averaging. This method improves the predictions made by the analyze component as well as the plan that adopts metaheuristic optimizing search to guide the adaptation decisions. Our empirical evaluation demonstrates the cost-effectiveness of our approach on an exemplar case study in the robotics domain.