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We show how to treat systematic uncertainties using Bayesian deep networks for regression. First, we analyze how these networks separately trace statistical and systematic uncertainties on the momenta of boosted top quarks forming fat jets. Next, we propose a novel calibration procedure by training on labels and their error bars. Again, the network cleanly separates the different uncertainties. As a technical side effect, we show how Bayesian networks can be extended to describe non-Gaussian features.