Characterization and propagation of uncertainties associated with limited data using a hierarchical parametric probability box

Uncertainty of random variables is commonly characterized from measurement data. In practice, data might be insufficient in order to obtain an accurate probability model. In this work, we assume that the type of distribution of the considered random variable is known a priori, and use a hierarchical parametric probability box (p‐box) – which is a set of distributions whose parameters are uncertain – to account for the limited data. Using Bayes' rule, knowledge about the variability of these parameters is updated. Propagation of these uncertainties through a computational model usually suffers from computational burden. A surrogate model approximating the computational model is constructed to reduce computational cost.