Add priorsense compatibility

[n-kall]

As discussed, this PR adds functionality for power-scaling sensitivity analysis via the priorsense package.
This PR is in progress, and needs to be kept up to date with any changes in priorsense before priorsense is on CRAN.

[paul-buerkner]

Thank you!

[paul-buerkner]

Hey @n-kall I just wanted to ask about the progress of this PR. Is there anything I can/should do at this point?

[paul-buerkner]

@n-kall do you need anything do move this PR forward? Not sure what the latest status of this was.

[n-kall]

@paul-buerkner This PR has taken been delayed for a while now, as I was getting the importance weighted moment matching in a neater state. Once the pareto-k diagnostics are merged into posterior (which should be quite soon), iwmm can go to CRAN and be used by priorsense. At that point the priorsense interface will be fixed and I'll update this PR.

[avehtari]

I'm curious about the status of this

[n-kall]

We've made quite some progress on a brmsfit method for iwmm at topipa/iwmm brmsfit-method branch. This has been the main hurdle and once done the brms compatibility with priorsense should be pretty much done.

[n-kall]

@paul-buerkner I've now updated the integration of priorsense based on how it is done for projpred, to finally get this PR ready. I think this is the simplest way to do things, but let me know if you think there is a more sensible way.

Essentially, the only user-facing function is create_priorsense_data.brmsfit but as explained in the docs, this is called automatically from priorsense functions and shouldn't need to be used directly.

I'd like to submit priorsense to CRAN soon, and I think it's best to move the brms-specific stuff from priorsense to brms before then (which is what this PR would do).

This is now ready for review.

[paul-buerkner]

Perfect! Will review and merge it this week.

[paul-buerkner]

I have now done some minor cleaning and the PR looks good to me.

Perhaps one thing we shall change is the example model such that it actually shows some prior sensitivity. Otherwise, the model is a bit boring since the powerscaling barely has any effect here. Would you mind changine the example in this direction?

In any case, I can only merge this PR into brms main once priorsense is on CRAN. This is because brms main needs to be CRAN releasable at any time which it is not if it suggests a package currently not on CRAN or another usable repo.

Also, don't forget to update the DESCRIPTION (new version number) and NEWS files

[paul-buerkner]

Also, would you mind adding a few tests based on the internally stored brms test models? At least for local runs (and skipped on CRAN).

[n-kall]

I think I addressed your comments, thanks! Let me know if there is more to change.
I'll work on getting priorsense on CRAN and let you know when it is and this can be merged.

[paul-buerkner]

Looks good! Thank you! As soon as priorsense is on CRAN, I will merge this PR.

[n-kall]

Priorsense (1.0.0) is now on CRAN so this can be merged (maybe bump the version number suggested to 1.0.0)

[paul-buerkner]

Excellent! Merging now. Thank you for all your work on this!