On data-based estimation of possibility distributions

Abstract

In this paper, we show how a possibilistic description of uncertainty arises very naturally in statistical data analysis. In combination with recent results in inverse uncertainty propagation and the consistent aggregation of marginal possibility distributions, this estimation procedure enables a very general approach to possibilistic identification problems in the framework of imprecise probabilities, i.e. the non-parametric estimation of possibility distributions of uncertain variables from data with a clear interpretation.

Multifidelity approaches for uncertainty quantification

“…For the estimation of the conditional possibility density functions, B‐splines and an elementary least‐squares formulation can be used according to Mäck and Hanss . This approach is motivated by the fuzzy regression formulation in Hose and Hanss and uses the correlation between and for the estimation. The additional information, in the form of the possibility density value , is only used to assign the corresponding value to the conditional density function after the regression analysis.…”