Introduction to imprecise probabilities

Since uncertainty is persistent in engineering analyses, this chapter aimed to introduce methods to describe and reason with under uncertainty in various scenarios. Probability theory is the most widely used methodology for uncertainty quantification for a long time and has proven to be a powerful tool for this task. Nevertheless, the construction of stochastic models relies on very fine information, such as large amount of observations, which is not always available. Without it, the constructed models are only very rough approximations of the real laws and may cause incorrect decisions. In this chapter, we introduce other types of models, based on the theory of imprecise probability, which we are able to construct and reason with under situations with limited available knowledge.