We recently finished two papers on imprecise probabilities.

The set structure of precision: coherent probabilities on Pre-Dynkin Systems

This shows a relationship between the set system of measurable events and imprecision of probabilities, and thus offers a novel way of generalising traditional probabilities that is potentially useful for a range of problems, including modelling "intersectionality"

and

Strictly Frequentist Imprecise Probability

This shows that one can develop and strictly frequentist semantics for imprecise probabilities, whereby upper previsions arise from the set of cluster points of relative frequencies. This means the theory is applicable to *all* sequences, not just stochastic ones. We also present a converse result that suggests that the theory is the "right" thing in the sense that every upper prevision can be derived from a (non-stochastic sequence). The proof of this fact is constructive.