Using inverse gamma as a prior of sigma in the regression model

Modeling
1

Hello, all,

For all the conversation in Stan, it appears that Cauchy distribution is the most recommended prior distribution for sigma.
However, I seem to get a lot of divergent transactions when I use Cauchy. I also tried gamma, which also is not better.

However, one day I tried inv-gamma and it seems to have done the magic with no divergence at all.

I mentioned this to someone, who told me that I can not use inv-gamma for sigma, it has to be the inverse sigma that is inv-gamma distributed.

Is this true? Is it forbidden to use inv-gamma on sigma?

Any insight will be appreciated.

Regards
Antony

2

Provided that the inverse gamma encodes appropriate information consistent with domain expertise I’m not sure if there’s any reason why you can’t use it. Have you tried simulating prior predictive distributions or prior push forwards to see if the prior implies unrealistic or impossible parameter/data values?

It could also be possible that your colleague is thinking from a conjugate, invariance, or “uninformative” perspective.

3

Thanks, js592.