The measurand value, the conclusions, and the decisions inferred from measurements may depend on the models used to explain and to analyze the results. In this paper, the problems of identifying the most appropriate model and of assessing the model contribution to the uncertainty are formulated and solved in terms of Bayesian model selection and model averaging. The computational cost of this approach increases with the dimensionality of the problem. Therefore, a numerical strategy to integrate over the nuisance parameters and to compute and to sample the measurand post-data distribution is also outlined.