Dear Stan experts,
I was wondering how to properly specify different priors and then decide which is more likely.
Let’s say there are two groups, treatment and control, and I wanted to fit the same model to them. Besides being interested in the difference in the posterior of the same parameter, I may also assume that the treatment group and the control group have different priors. E.g., the control group may have a belief of some normal pain, but the treatment group may have a lower belief of pain (belief of reduced pain).
Assuming the parameter is between 0 and 1, and what I have in mind is to do a grid search with a step of 0.01, and set the prior to be centered around the step, thus 100 prior specifications; then I fit 100 stan models to the same data (treatment or control), with the 100 priors, and lastly do model comparison to find out which prior value is more likely to the data.
Does the above approach sound valid? Or completely wrong? I would imagine this type of question is generic and I highly appreciate if someone could give a hint to solve it more properly.
Many thanks in advance,