We designed a processor microarchitecture [1] at the University of Cambridge, inspired by Uncertain<T> (James Bornholt) and related work. In addition to assuming parametric distributions (e.g., Gaussian, Rayleigh), it lets you load arbitrary sets of samples into registers/memory so program values are carried and propagated as nonparametric distributions through ordinary arithmetic.
A spin-off, Signaloid, is taking this technology to market. I'm also researching using this in state estimation (e.g., particle filters).