Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

9.1 Open Scientific Challenges

Once probabilistic computation as well as sensitivity analysis science and techniques start disseminating, the need for careful handling of data and expertise designed to perform accountable input uncertainty modelling becomes all the more important. Indeed, it appears as the typical top priority for industrial applications. One is likely to ask what type of input probabilistic model should be fed into uncertainty and sensitivity analysis when considering largely missing data sets. In that respect, Bayesian settings still have much further to go, regarding notably the issue of choosing accountable priors in the risk context where distribution tails are important. However, Bayesian approaches should not disregard the attention paid to the underlying identifiability issues that are essential in the risk context. The development of sophisticated physical-numerical models spurred on by computational availability tends to enrich input parameterisation much quicker than the true amount of data available to calibrate the input distributions: an elementary requirement, however, is that modelling should not increase risk.

There is a delicate issue regarding the modelling of input distribution tails when quantities of interest involved in the study are extreme quantiles or exceedance probabilities. While the extreme value theory is quite abundant and consensual when dealing with scalar random variables (cf. the review by Coles, 2001), the modelling of multivariate ...