Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty
regarding various physical quantities in a well-defined and self-contained manner. Utilising modern
tools, such Bayesian models can be constructed with a remarkable flexibility, leaving us totally free
to carefully choose which assumption should be strictly enforced and which should on the contrary
be relaxed. The practical evaluation of these assumptions, together with the data-driven selection
or averaging of models, also appears in a very natural way.
In this presentation, I discuss its application in the context of lattice QCD and its common
statistical problems. As a concrete illustration, I present a few parametric and non-parametric
hierarchical models applied to actual correlator data, from single exponential fits to spectral functions.