TOWARDS A GENERAL THEORY FOR DATA-BASED POSSIBILISTIC PARAMETER INFERENCE

This paper unifies several recent results from possibilistic uncertainty analysis in order to contribute to a general theory of possibilistic parameter estimation by providing an exemplary procedure to estimating possibilistic distributions of model parameters from samples of an aggregated output quantity. This task is accomplished by dividing the problem in two subproblems. In the first step, the output samples are represented in a structured manner by a possibility distribution. The second step deals with the backpropagation of the output distribution through a model, thus arriving at a distribution of the input quantity to be estimated. The theoretical basis for this two-step scheme lies in the theory of imprecise probabilities, giving the computed distributions an immediate and meaningful interpretation. It is intended to provoke the development of a novel theory complementary to classical statistics.