@ggluck Deterministic is not a random variable, it is correspondent to represent a deterministic variable (as a combination of several RVs). We can use deterministic variables to capture the transformations to the random variables and store them in the trace.
However, if you can fix the deterministic using observed then there is no point of storing it in the trace.
Please look this git issue for more details - https://github.com/pymc-devs/pymc3/issues/1971
Why do you want to use deterministic at the end? And how are you going to determine the bounds using a single observed value. I think you should provide multiple actual number of contaminated samples from multiple experiments.
I don’t think that I can help you with your exact usecase, if you can provide the probabilistic model of your usecase then someone can help you.