Pragmatic aspects of uncertainty propagation: A conceptual review

• We analyze propagation of uncertainty through computationally costly models.
• Practicality limits the number of simulations that can be used.
• Specifying input uncertainty can be more important than interpolating responses.
• Separating these tasks allows for flexibility in choosing simulations.
• We compare polynomial and Gaussian-process interpolation.

When quantifying the uncertainty of the response of a computationally costly oceanographic or meteorological model stemming from the uncertainty of its inputs, practicality demands getting the most information using the fewest simulations. It is widely recognized that, by interpolating the results of a small number of simulations, results of additional simulations can be inexpensively approximated to provide a useful estimate of the variability of the response. Even so, as computing the simulations to be interpolated remains the biggest expense, the choice of these simulations deserves attention. When making this choice, two requirement should be considered: (i) the nature of the interpolation and (ii) the available information about input uncertainty. Examples comparing polynomial interpolation and Gaussian process interpolation are presented for three different views of input uncertainty.