Towards fully bayesian analyses in Lattice QCD

We present a promising method to learn physical parameters from a bayesian inference, using modern tools to replace both our traditional fits and the way errors are computed and propagated. A few models are built as illustrations for a realistic case with Lattice QCD data, and appear to extract a lot of information with good stability. We discuss the evaluation of these models with either a fully bayesian approach or information criteria, as well as the model-building challenges which remain to be solved.