Switching to broadcasting random walk

[seabbs]

Description

Following on from #746 this PR switches to broadcasting for the random walk parameterizations. It also adds docs and tests.

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 d94e55e is merged into main:

• ✔️default: 42.5s -> 41.4s [-24.51%, +19.32%]
• ✔️no_delays: 45.4s -> 48.9s [-8.07%, +23.47%]
• ✔️random_walk: 9.93s -> 9.54s [-16.52%, +8.61%]
• ✔️stationary: 23.6s -> 19.7s [-50.29%, +16.86%]
• ✔️uncertain: 1.19m -> 1.19m [-32.79%, +33.36%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[jamesmbaazam]

Thanks @seabbs. LGTM. Thanks for adding the tests and documentation.

To confirm that I understood everything here. This was more of a refactoring exercise to use more elegant stan tricks right? I noticed most of the right hand side code is a better rewrite of the deleted code using what we would call vectorization in R parlance.

[seabbs]

yes and to ideally reduce compilation and run time (which I think it does a tiny bit)

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 7822fe8 is merged into main:

• ✔️default: 45.1s -> 41.8s [-24.03%, +9.1%]
• ✔️no_delays: 48.4s -> 50.8s [-20.71%, +30.28%]
• 🚀random_walk: 10s -> 8.72s [-25.79%, -0.65%]
• ✔️stationary: 20.1s -> 20.2s [-18.99%, +20.08%]
• ✔️uncertain: 1.16m -> 1.06m [-17.68%, +1.32%]
  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 8457a9e is merged into main:

• 🚀default: 51.6s -> 44.2s [-25.39%, -3.16%]
• ✔️no_delays: 52.1s -> 50.4s [-18.4%, +11.55%]
• ✔️random_walk: 9.89s -> 9.79s [-10.02%, +7.99%]
• ✔️stationary: 20.9s -> 20.3s [-14.35%, +8.79%]
• ✔️uncertain: 1.07m -> 1.17m [-13.96%, +33.69%]
  Further explanation regarding interpretation and methodology can be found in the documentation.