Reference for exponential prior for non-hierarchical models

#1

Hi all,

The wiki at https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations mentions
the exponential(10) as a possible weakly informative prior for the standard deviation in a non-hierarchical model. Does anyone have a reference to a paper discussing this option? It would be helpful when I’m writing up my analysis plan to better convince reviewers still wedded to the uninformative-prior paradigm.

I know of the PC prior paper by Simpson et al, but I’m not sure their reasoning applies in a non-hierarchical context.

Best regards,
Gustaf

#2

That’s exponential(0.1) since it is parameterized in terms of its rate in Stan.

There are plenty of papers that use exponential priors. I don’t know of any that say having a rate of 0.1 is a good idea; Andrew just made that up.

Since there are no uninformative priors over the positive real numbers, if you run into a reviewer that is wedded to the uninformative-prior paradigm, I don’t think having a footnote is going to make much difference.

#3

Thanks!

I’m working in a field (network meta-analysis) where things are quite heavily regulated, and there are technical guidelines for the modelling process, including winbugs/jags code with the classic N(0,10^4) type semi-flat priors, combined with some U(0,5) for some standard deviations (see the appendix of NICE TSD2 if you’re interested). Since it’s published as an official guideline, if you stick with their code, you’re fine. But if you deviate, there’s a risk of getting pushback, so having some (any) ref for why a weak exponential is a good idea would be useful backing (if nothing else to comfort the clients who will submit our models).

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#4

If you’re going to alter NICE TSD priors your best bet is to use informative priors from Turner (2012?). If your estimates are blowing up because of the U(0, 5) you won’t get pushback using these since they are empirically estimated from Cochrane reviews

#5

I would cite McElreath’s book on the exponential prior in hopes that the regulators read it.

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