Joe Zhao writes:
I am trying to fit my data using the scaled inverse wishart model you mentioned in your book, Data analysis using regression and hierarchical models. Instead of using a uniform prior on the scale parameters, I try to use a log-normal distribution prior. However, I found that the individual coefficients don’t shrink much to a certain value even a highly informative prior (with extremely low variance) is considered. The coefficients are just very close to their least-squares estimations. Is it because of the log-normal prior I’m using or I’m wrong somewhere?
My reply: If your priors are concentrated enough at zero variance, then yeah, the posterior estimates of the parameters should be pulled (almost) all the way to zero. If this isn’t happening, you got a problem. So as a start I’d try putting in some really strong priors concentrated at 0 (for example, N(0,.1^2)) and checking that you get a sensible answer. If not, you might well have a bug. You can also try fake data simulation.