Keywords: Bayesian approach, imprecise probabilities, uncertainty quantification.

e challenge of dealing with information that is limited, subjective, fragmentary and vague. Various approaches have been developed over the past decades to address this challenge, including (not exhaustively) the Bayesian and imprecise probability approach. In this paper we review both developments from a conceptual point of view and discuss their capabilities underlined with illustrative examples. In this context we point out some complementary features of these two approaches. The Bayesian approach integrates the knowledge from expert judgement, modelling assumptions and measured data through the machinery of conditional probability. The imprecise probability approach addresses issues such as vagueness, indeterminacy and imprecision with set-theoretical models and combine these in a manner consistent with probability logic to arrive at bounds on probabilities. Both concepts have demonstrated their usefulness in various engineering applications. The decision towards which concept, or even a combination of both, to use in practice depends on the available information and on the purpose of the analysis. Both concepts will be discussed to nurture an overall understanding of their features and capabilities and to resolve conflicting views.

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