In this paper, we consider the problems of identifying the most appropriate model for a given physical system and of assessing the model contribution to the measurement uncertainty. The above problems are studied in terms of Bayesian model selection and model averaging. As the evaluation of the “evidence” [Formula: see text], i.e., the integral of Likelihood × Prior over the space of the measurand and the parameters, becomes impracticable when this space has [Formula: see text] dimensions, it is necessary to consider an appropriate numerical strategy. Among the many algorithms for calculating [Formula: see text], we have investigated the ellipsoidal nested sampling, which is a technique based on three pillars: The study of the iso-likelihood contour lines of the integrand, a probabilistic estimate of the volume of the parameter space contained within the iso-likelihood contours and the random samplings from hyperellipsoids embedded in the integration variables. This paper lays out the essential ideas of this approach.