I’m using Stan for what I suspect may be an unusual purpose: fitting a material behavior model to stress-strain curve data that I got from a co-worker. The reason I’m using Stan rather than just doing least-squares fitting is that I’m also trying to get probability distribution functions for the parameters of the model.
Now this material model has several fitting parameters, but a few of them aren’t “pure” fitting parameters, but rather have physical meaning: namely the yield strength, Young’s modulus, and melting temperature. I could treat those parameters purely as data, but the catch is that there is some uncertainty in those parameters; they may vary from one batch of material to another. Worse, the information on the yield strength and elastic modulus is somewhat spotty, with a fairly wide spread of values.
So far, what I’ve been doing is assigning more-or-less plausible lower and upper bounds for these parameters, and leaving the prior distribution for the parameters as the default (uniform). Unfortunately, if I use “soft” constraints, such as setting the prior distribution for a parameter to a normal distribution centered around a plausible mean value of a parameter, the resulting probability distributions for those parameters are decidedly improbable. However, I’m not sure that using hard upper and lower bounds is a good choice either. Feels like there’s a better option that I’m just missing due to lack of experience with Bayesian data analysis.
Any idea how to deal with these particular kinds of uncertain parameters?