Introduction to Imprecise Probabilities

Acknowledgements

We are very grateful to Erik Quaeghebeur for inspiring discussions about the background of Section 7.4.

¹ In particular, we are very sloppy with respect to finite versus -additivity of underlying precise probabilities, and aspects of measurability. See in particular [323] for a mathematically rigorous exposition of the framework applied here.

² In a broader sense, statistical inference aims to infer general laws not necessarily confined to the population the sample was drawn from. Consider, e.g., a medical study conducted to answer the question if some (new) medical treatment works generally better than the (standard) treatment . Such studies are based on the performance of treatments and in the participants of a clinical trial (the sample). Here, the goal is not to infer the performance of and in the population the study participants were drawn from (which is often ...