A bit of an odd question perhaps, so please correct my thinking if I’m looking at this the wrong way.
I want to estimate a normal regression model with two covariates A and B:
y \sim N(\beta_0 + \beta_1 A + \beta_2 B,\sigma)
However, I do not currently have any data which I can use to estimate \beta_1 from, but I know the distribution of \beta_1 from a previous experiment. For instance, I may know that \beta_1 \sim N(-0.7,0.2).
I want to tell STAN about the knowledge I have about \beta_1, but I do not want STAN to treat this knowledge as a prior and expect data to guide the sampling from the posterior. I want STAN to treat my information as the posterior for \beta_1 and use this to estimate the model and sample the posterior for \beta_0 and \beta_2.
Can this be done, and if so, how would I code this up?
Thanks in advance.