Appropriate Gamma prior for ARD regression


I am implementing ARD regression problems and I got a question. It seems like we usually imply very flat gamma priors for the ARD regression problem such as Gamma(0.01,0.01) as parameter’s variances. The prior shape can be considered as flat; however, isn’t it we are implying “most of variables are highly relevant to Y”? This is because a variable’s coefficient parameter distribution can only go to 0 when the mean of gamma is increasing (which means if the variables are relevant, variance should be small).

In this regard, I was just wondering if I can use Gamma(1,1) or Gamma(2,0.01) priors for the ARD regression models. Or how do you guys approaches for these issues on what appropriate priors are.



Hi. Have you tried prior calibration via prior predictive checks? Here’s a PyMC entry on prior predictives: Prior and Posterior Predictive Checks — PyMC 5.10.3 documentation . Hope it helps.