Suppose I have a linear regression problem y=a1x1+a2x2+b. I want to evaluate coefficients a1 and a2 by Bayesian inference while b at a frequentist view, i.e. treat it as a simple paramter instead of a distribution. Is there any way to do that? Maybe I can set b a normal prior with a very small standard deviation, but is there more efficient way?

Yes. I recommend the linear mixed effects model tutorial. A mixed effects model is precisely one where you perform Bayesian inference over certain parameters (“random effects”) while point estimating others (“fixed effects”).

That’s cool. Thank you