  Gibbs states are familiar from statistical mechanics, yet their use is not
limited to that domain. For instance, they also feature in the maximum entropy
reconstruction of quantum states from incomplete measurement data. Outside the
macroscopic realm, however, estimating a Gibbs state is a nontrivial inference
task, due to two complicating factors: the proper set of relevant observables
might not be evident a priori; and whenever data are gathered from a small
sample only, the best estimate for the Lagrange parameters is invariably
affected by the experimenter's prior bias. I show how the two issues can be
tackled with the help of Bayesian model selection and Bayesian interpolation,
respectively, and illustrate the use of these Bayesian techniques with a number
of simple examples.
