Add laplace and pathfinder approximate inference

[sbfnk]

Description

This PR closes #403.

It adds laplace and pathfinder approximations when the cmdstanr backend is used. Will need a bit more testing but they both seem more robust than the standard variational inference version. If this is confirmed we could add a note to e.g. one of the vignettes to say that these could be used to get an approximate idea before running exact inference for production.

fit_model_with_vb has been re-used and re-named for this but as it was really an internal function I didn't start a deprecation cycle.

Initial submission checklist

• My PR is based on a package issue and I have explicitly linked it.
• I have tested my changes locally (using devtools::test() and devtools::check()).
• I have added or updated unit tests where necessary.
• I have updated the documentation if required and rebuilt docs if yes (using devtools::document()).
• I have followed the established coding standards (and checked using lintr::lint_package()).
• I have added a news item linked to this PR.

After the initial Pull Request

• I have reviewed Checks for this PR and addressed any issues as far as I am able.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 9545b8a is merged into main:

• ✔️default: 35.7s -> 37.2s [-12.19%, +20.85%]
• ✔️no_delays: 40.6s -> 41.2s [-10.54%, +13.33%]
• ✔️random_walk: 10.6s -> 10.4s [-10.38%, +6.58%]
• ✔️stationary: 32.6s -> 2.18m [-460.69%, +1061.34%]
• ✔️uncertain: 54.9s -> 56.3s [-11.61%, +16.48%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[seabbs]

LGTM. I think marking them as experimental (as they are) is good enough

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 93c072d is merged into main:

• ✔️default: 38.9s -> 36.3s [-26.48%, +13.22%]
• 🚀no_delays: 45.5s -> 40.7s [-19.86%, -1.14%]
• ✔️random_walk: 10.1s -> 10.3s [-6.11%, +10.12%]
• ✔️stationary: 23.2s -> 20.3s [-32.85%, +8.2%]
• ✔️uncertain: 56.7s -> 59s [-5.68%, +13.47%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if e9eab37 is merged into main:

• ✔️default: 33.5s -> 35.6s [-12.79%, +25.33%]
• ✔️no_delays: 44.4s -> 43s [-19.21%, +12.73%]
• ✔️random_walk: 18.6s -> 11.1s [-143.06%, +62.31%]
• ✔️stationary: 22.5s -> 21.6s [-17.33%, +9.83%]
• ✔️uncertain: 1.01m -> 55.7s [-24.15%, +8.32%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if f7ded41 is merged into main:

• ❗🐌default: 32.8s -> 40.5s [+6.17%, +40.74%]
• ✔️no_delays: 41.8s -> 45.5s [-1.7%, +19.55%]
• ✔️random_walk: 9.68s -> 10s [-6.57%, +13.59%]
• ✔️stationary: 19.5s -> 21.2s [-4.33%, +22.22%]
• ✔️uncertain: 55.3s -> 59.7s [-9.26%, +24.93%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 5a27186 is merged into main:

• 🚀default: 36s -> 30.9s [-25.72%, -2.47%]
• ✔️no_delays: 42.7s -> 42.2s [-13.57%, +11.09%]
• ✔️random_walk: 9.66s -> 10.1s [-5.86%, +15.77%]
• ✔️stationary: 22.5s -> 19.8s [-45.05%, +21.26%]
• ✔️uncertain: 1.08m -> 52.2s [-68.55%, +29.13%]
  Further explanation regarding interpretation and methodology can be found in the documentation.