move lengthscale prior to dist_spec

[sbfnk]

Description

This PR closes #878.

In order for there to be a prior choice that applies across applications it rescales the lengthscale with half the length of the time series as done in Riutort-Mayol et al. It also fixes the minimum to zero (for now) which was previously the default but changeable.

Todo before merging:

• test with different data sets that this works and doesn't affect our ability to fit the model
• update documentation

Todo after merging (future PRs):

• re-do the exploration in not for merging: Explore divergent transitions #855
• maybe update the parameter names in places? We've got a bit of a mixture of rho/ls so need to decide in which places we want this to be the

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 e2afb31 is merged into main:

• ✔️default: 22.9s -> 23.4s [-12.53%, +17.13%]
• ✔️no_delays: 26s -> 35.3s [-12.77%, +83.49%]
• ✔️random_walk: 9.83s -> 10.5s [-4.76%, +17.56%]
• ✔️stationary: 14.8s -> 14.2s [-21.38%, +12.45%]
• ✔️uncertain: 37.1s -> 37.8s [-7.64%, +11.03%]
  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 01bfc98 is merged into main:

• ✔️default: 22.6s -> 24.2s [-5.92%, +20.06%]
• 🚀no_delays: 28.3s -> 26.1s [-15.49%, -0.29%]
• ✔️random_walk: 10.7s -> 9.87s [-18.91%, +3.14%]
• ✔️stationary: 14.1s -> 13.9s [-13.76%, +10.35%]
• ✔️uncertain: 39.8s -> 37s [-19.91%, +5.87%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[sbfnk]

test with different data sets that this works and doesn't affect our ability to fit the model

The vignettes show no meaningful change in results or number of divergent transitions. Benchmarks also show no significant change in performance. If this looks correct to people we can probably merge and explore further building on this.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 11f1dca is merged into main:

• ✔️default: 24.2s -> 22.6s [-26.44%, +13.02%]
• ✔️no_delays: 28s -> 32.2s [-21.73%, +52.04%]
• ✔️random_walk: 9.96s -> 10.1s [-2.72%, +5.86%]
• ✔️stationary: 14s -> 13.8s [-18.23%, +14.79%]
• ✔️uncertain: 37.6s -> 40.4s [-15.55%, +30.94%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[jamesmbaazam]

@seabbs Do you want to take this one?