Appropriate Gamma prior for ARD regression

Questions v5
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1

Hello,

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.

Thanks,

Jay

2

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.

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