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This paper presents a novel compositional multidisciplinary uncertainty analysis methodology for systems with feedback couplings, and model discrepancy. Our approach incorporates aspects of importance resampling, density estimation, and Gibbs sampling to ensure that, under mild assumptions, our method is provably convergent in distribution. A key feature of our approach is that disciplinary models can all be executed offline and independently. Offline data is synthesized in an online phase that does not require any further model evaluations or any full coupled system level evaluations. We demonstrate our approach on a simple aerodynamics-structures system.