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In this talk I will discuss how Bayesian priors derived from first principles, for instance analyticity and unitarity, can be used to complement theory computations of hadron observables. I will demonstrate the ideas for the analysis of lattice-QCD simulations of exclusive as well as inclusive semileptonic B-meson decay. In the former case, the use of Bayesian inference allows for formulating a model- and truncation independent parameterisation of hadronic form factors. In the latter case, QFT priors allow to tackle the computation of the inclusive decay rate for the first time.