How to define and interpret a probability in a risk and safety setting

This paper is a discussion paper and consists of two parts: first an introduction by the Associate Editor Genserik Reniers discussing the reason behind this article and classifying such a type of paper, and second the contribution by Terje Aven, with following abstract:The application of probability is of paramount importance for the risk and safety fields. But few of the papers in these fields explain what the probabilities introduced mean. The rules of probability are referred to, but very rarely do we see the authors of these papers defining or reflecting on how the probabilities are to be understood. The justification for this practice is that the scientific contributions mainly relate to computation of probability, and the calculus is independent of the interpretations. However, if the probabilistic analysis is to be implemented in practice, the meaning of the probabilities is essential. The probability numbers then have to be communicated, and it must be clear what a probability of 0.2 means compared to (say) 0.3. The purpose of the present paper is to point to the main alternative interpretations available and provide arguments for the use of some of these and the rejection of others, in a risk and safety context. Special focus is placed on subjective probabilities and what is referred to as value-based interpretations of such probabilities (which include betting and utility-based definitions). A main aim of the paper is to argue against these value-based interpretations and for the use of subjective probabilities understood with a reference to an uncertainty standard such as an urn, as strongly advocated by Dennis Lindley for more than 30 years. Many probabilists are unfamiliar with this interpretation of probability.

► A discussion of relevant probability interpretations for the risk and safety fields.
► It is argued against value-based interpretations of subjective probabilities.
► These value-based interpretations cover betting and utility-based definitions.
► Arguments provided for an uncertainty standard interpretation.