Probability boxes on totally preordered spaces for multivariate modelling

Probability boxes (pairs of cumulative distribution functions) are among the most popular models used in imprecise probability theory. In this paper, we provide new efficient tools to construct multivariate pboxes and develop algorithms to draw inferences from them. For this purpose, we formalise and extend the theory of p-boxes using lower previsions. We allow p-boxes to be defined on arbitrary totally preordered spaces, hence thereby also admitting multivariate pboxes. We discuss the construction of multivariate pboxes under various independence assumptions. An example demonstrates the practical feasibility of our results.