  Imprecise probability is concerned with uncertainty about which probability
distributions to use. It has applications in robust statistics and elsewhere.
Imprecise probability can be modelled in various ways, including by convex sets
of probability distributions.
  We look at programming language models for imprecise probability. Our
desiderata are that we would like our model to support all kinds of
composition, categorical and monoidal, in other words, guided by dataflow
diagrams. Another equivalent perspective is that we would like a model of
synthetic probability in the sense of Markov categories.
  There is already a fairly popular monad-based approach to imprecise
probability, but it is not fully compositional because the monad involved is
not commutative, which means that we do not have a proper monoidal structure.
In this work, we provide a new fully compositional account. The key idea is to
name the non-deterministic choices. To manage the renamings and disjointness of
names, we use graded monads. We show that the resulting compositional model is
maximal. We relate with the earlier monad approach, showing that we obtain
tighter bounds on the uncertainty.
