I mean something like what @jessegrabowski proposed, or what you mentioned here:
(I’m also having one of my students try adding artificial “observational noise” to the model, which would probably cure the problem by making any “impossible” observations yi for a given value of Θ merely “very very unlikely”. He’s making progress on it, but if we stall out on that idea I might post another thread here about how to implement it.)
I think the “artificial noise” approach is easier to interpret, so I think I’d try that one first?
I wish we had have a better solution. More complicated constraints on the posterior come up from time to time, and they are mathematically well defined, but unfortunately I’m not aware of any algorithms that can really deal with them well.