Possibly extreme, probably not: Is possibility theory the route for risk‐averse decision‐making?

Abstract

AbstractEnsemble forecasting has become popular in weather prediction to reflect the uncertainty about high‐dimensional, nonlinear systems with extreme sensitivity to initial conditions. By means of small strategical perturbations of the initial conditions, sometimes accompanied with stochastic parameterisation schemes of the atmosphere–ocean dynamical equations, ensemble forecasting aims at sampling possible future scenario and ideally at interpreting them in a Monte‐Carlo‐like approximation. Traditional probabilistic interpretations of ensemble forecasts do not take epistemic uncertainty into account nor the fact that ensemble predictions cannot always be interpreted in a density‐based manner due to the strongly nonlinear dynamics of the atmospheric system. As a result, probabilistic predictions are not always reliable, especially in the case of extreme events. In this work, we investigate whether relying on possibility theory, an uncertainty theory derived from fuzzy set theory and connected to imprecise probabilities, can circumvent these limitations. We show how it can be used to compute confidence intervals with guaranteed reliability, when a classical probabilistic postprocessing technique fails to do so in the case of extreme events. We illustrate our approach with an imperfect version of the Lorenz 96 model and demonstrate that it is promising for risk‐averse decision‐making.