I have a parameter space that is M dimensional. My prior on the parameters is independent N(0,1) in that space. My observation space is a full rank linear transformation of that parameter space. If the parameters are P, I make observations of RP. Actually, that's not quite right. What happens is I make a single observation of a lower dimensional subset of RP. E.g. I have a single observation of the 2nd dimension of RP. What I want to do is take that observation of a subset of RP and use it to update my beliefs about the distribution of the full M-dimensional parameter space. Then, eventually, I want to generate samples of my parameter space that are consistent with this updated posterior and then transform those into observation space to get "samples in observation space that are consistent with the restriction I provided in my training step". I know how to do this in Numpyro if I make up some (fictitious) observation noise (i.e. I say I don't observe R * P but, instead, R * P + noise). But I don't like that hack. Any better thoughts?
I tried essentially imposing a set of "constraints" using numpyro.factor()'s log density.