Incorporate external knowledge of Noise-Related quantity(Potentials?)

Hi there! I am trying to incorporate in my model the following thing: I have a model for expected value and likelyhood for a quantity x; I also have another quantity y, measured a posteriori, that I know is highly correlated with how much x deviates from my model. Since it’s a posteriori obviously I can’t put it directly in the model, but what I would like to do is to weight my observations with respect to the value of y, i.e. the bigger the y the less important the observation.

How do I do it? I tried for a bit with a potential, but the correct syntax is obscure to me: I believe there has to be a way of doing such a thing by directly modifying the likelyhood function, but I have no idea how.