http://areshenkblog.com/priors-for-variance-parameters-in-hierarchical-models/ ]]>

The code is linked. Try it!! Email me and I’ll add another table.

]]>All of these have mode x, but they are tighter and tighter around x rather than having the mode being pulled farther and farther to the right. This makes much better sense to me, the point is you have some prior information that the parameter should be near some value x, and N becomes a “concentration” parameter saying how far away from x you’re willing to allow Stan to look.

]]>Regarding bias, I guess it depends. If we actually have prior information justifying pulling tau (in this case) away from zero in the prior then yeah that’s just a prior. But if we don’t have that prior knowledge then a prior like this seems like a trade off between bias and ease of computation. Of course, we make those trade offs all the time but the beauty of the non-centered parameterization is that it sidesteps the trade off in this case.

]]>I can do it for the log-normal if you want! Any suggestions for a ladder of parameters?

>Also, I disagree that the priors “bias the group standard deviation.” If the prior information is real, the priors aren’t biasing anything! That’s Bayesian inference for you.

It gives you a massively different set of values, and I suspect that this will tank predictive performance. But I can’t check that without a proper simulation study and it’s a Friday afternoon.

]]>We did use the zero-avoiding gamma(2) priors for point estimation, but here I was actually thinking of stronger priors, maybe even lognormal, that really do exclude zero for real. I’d discussed this with Jonah in the ofc but I guess that didn’t make it into my post.

Also, I disagree that the priors “bias the group standard deviation.” If the prior information is real, the priors aren’t biasing anything! That’s Bayesian inference for you.

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