Model selection in the average of inconsistent data: an analysis of the measured Planck-constant values

When the data do not conform to the hypothesis of a known sampling variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require one to find what measurand value is the most trustworthy. Bayesian inference is reviewed here, to assign probabilities to the possible measurand values. Different hypotheses about the data variance are tested by Bayesian model comparison. Eventually, model selection is exemplified in deriving an estimate of the Planck constant.