Robustness as a criterion for selecting a probability distribution under uncertainty

Abstract

© Springer International Publishing AG 2017. Often, we only have partial knowledge about a probability distribution, and we would like to select a single probability distribution ρ(x) out of all probability distributions which are consistent with the available knowledge. One way to make this selection is to take into account that usually, the values x of the corresponding quantity are also known only with some accuracy. It is therefore desirable to select a distribution which is the most robust—in the sense the x-inaccuracy leads to the smallest possible inaccuracy in the resulting probabilities. In this paper, we describe the corresponding most robust probability distributions, and we show that the use of resulting probability distributions has an additional advantage: it makes related computations easier and faster.