Hi Alex,
Thanks for your answer! I will look at the prior predictive checks idea!
I usually use a Jeffrey prior for variance parameters, when it is possible to do the computation analytically.
In the case of MCMC, it is not possible to use it because it is improper. But what do you think of the choice of the inverse gamma prior with very small \alpha and \beta? I believe that the limit of the inverse gamma is the Jeffrey’s prior when \alpha and \beta approach 0, isn’t it?