Robust calibration of numerical models based on relative regret

Classical methods of parameter estimation usually imply the minimisation of an objective function, that measures the error between some observations and the results obtained by a numerical model. In the presence of random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced. In this paper, we are going to present how to take into account those uncertainties by defining a family of calibration objectives based on the notion of relative-regret with respect to the best attainable performance given the uncertainties and compare it with the minimum in the mean sense, and the minimum of variance.