Inferring a possibility distribution from empirical data

Several transformations from probabilities to possibilities have been proposed. In particular, Dubois and Prade’s procedure produces the most specific possibility distribution among the ones dominating a given probability distribution. In this paper, this method is generalized to the case where the probabilities are unknown, the only information being a data sample represented by a histogram. It is proposed to characterize the probabilities of the different classes by simultaneous confidence intervals with a given confidence level 1 − α. From this imprecise specification, a procedure for constructing a possibility distribution is described, insuring that the resulting possibility distribution will dominate the true probability distribution in at least 100(1 − α)% of the cases. Finally, a simple efficient algorithm is given which makes the computations tractable even if the number of classes is high.