jgabry
commented
8 years ago Hi Juho, thanks for the suggestion. It seems like a good idea to me. @bgoodri what do you think?
For (1) we could preserve backwards compatibility if we add a second argument to hs, something like hs(df=3, global_scale = 1).
For (2) I agree that some more research is probably needed, but the coding shouldn't be too bad.
On Monday, September 5, 2016, Juho Piironen notifications@github.com wrote:
Summary:
I would like a possibility of adjusting the scale and degrees of freedom for the global parameter tau in the hierarchical shrinkage (HS) prior. Description:
We discussed the use of HS-prior for regression models in our technical report (Piironen and Vehtari, 2015) after which it was added to rstanarm, which is great! However, the current version allows only tuning the degrees of freedom for the local scale parameters lambda_j, but does not allow changing the prior for the global parameter tau which is given half-Cauchy prior with scale 1. For some datasets, this prior for tau gives too much mass for implausibly large values, and therefore favors solutions with many of the regression coefficients different from zero (I'm working on a paper that would give a recommendation on how to specify prior for tau based on our guess for the number of relevant variables in the data). A suggestion:
1) Replace tau ~ half-Cauchy(0,1) with tau ~ half-t_nu(0,s), and allow user to change the degrees of freedom nu and scale s (by default they can be set to 1 and 1, however).
2) In regression, there are theoretical considerations why one might want to use prior tau ~ half-t_nu(0,s*sigma), where sigma is the noise std. So it would be nice to have this alternative too.
I believe item 1) should be rather easy and quick to implement but would be very useful by providing more control over tau. However, item 2) might require more extra work and there might be some practical difficulties in the implementation and use I'm not aware of. Thus I'm proposing it only as something you could consider in the future, and I think item 1) would be more important to have at the moment.
Thanks a lot! References:
J. Piironen, A. Vehtari (2015). Projection predictive variable selection using Stan+R, http://arxiv.org/abs/1508.02502
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bgoodri
ariddell
jpiironen
Summary:
I would like a possibility of adjusting the scale and degrees of freedom for the global parameter tau in the hierarchical shrinkage (HS) prior.
Description:
We discussed the use of HS-prior for regression models in our technical report (Piironen and Vehtari, 2015) after which it was added to rstanarm, which is great! However, the current version allows only tuning the degrees of freedom for the local scale parameters lambda_j, but does not allow changing the prior for the global parameter tau which is given half-Cauchy prior with scale 1. For some datasets, this prior for tau gives too much mass for implausibly large values, and therefore favors solutions with many of the regression coefficients different from zero (I'm working on a paper that would give a recommendation on how to specify prior for tau based on our guess for the number of relevant variables in the data). A suggestion:
1) Replace tau ~ half-Cauchy(0,1) with tau ~ half-t_nu(0,s), and allow user to change the degrees of freedom nu and scale s (by default they can be set to 1 and 1, however).
2) In regression, there are theoretical considerations why one might want to use prior tau ~ half-t_nu(0,s*sigma), where sigma is the noise std. So it would be nice to have this alternative too.
I believe item 1) should be rather easy and quick to implement but would be very useful by providing more control over tau. However, item 2) might require more extra work and there might be some practical difficulties in the implementation and use I'm not aware of. Thus I'm proposing it only as something you could consider in the future, and I think item 1) would be more important to have at the moment.
Thanks in advance!
References:
J. Piironen, A. Vehtari (2015). Projection predictive variable selection using Stan+R, http://arxiv.org/abs/1508.02502