Change pareto functions to return unnamed numerics

[n-kall]

Summary

This changes pareto_* functions to no longer return named numeric values if there is just a single value output. This applies to pareto_khat, pareto_khat_threshold, pareto_min_ss, and pareto_convergence_rate.

pareto_diags returns a named vector of all of these. And pareto_smooth is not affected by this.

This also changes the return type of pareto_khat to be an unnamed numeric rather than a list, which would require a change in loo (specifically E_loo). As there is already an issue that needed to be worked around (stan-dev/loo/issues/263) I think this is worth addressing now.

This would close #359 and #346

Copyright and Licensing

By submitting this pull request, the copyright holder is agreeing to license the submitted work under the following licenses:

• Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
• Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

[github-actions[bot]]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 86c8fba71b1be6cf01e847cb7901fd384ab4fa2b is merged into master:

• :heavy_check_mark:as_draws_array: 154ms -> 152ms [-2.74%, +0.37%]
• :heavy_check_mark:as_draws_df: 73.2ms -> 73.9ms [-0.41%, +2.37%]
• :heavy_check_mark:as_draws_list: 173ms -> 173ms [-1.09%, +1.01%]
• :heavy_check_mark:as_draws_matrix: 69.7ms -> 69.7ms [-1.26%, +1.32%]
• :heavy_check_mark:as_draws_rvars: 86.7ms -> 86.3ms [-1.34%, +0.46%]
• :heavy_check_mark:summarise_draws_100_variables: 718ms -> 716ms [-1.17%, +0.44%]
• :heavy_check_mark:summarise_draws_10_variables: 120ms -> 120ms [-1%, +0.58%] Further explanation regarding interpretation and methodology can be found in the documentation.

[paul-buerkner]

Looks good to me. Do you want to make any changes before I merge?

[n-kall]

I think it's ready

[paul-buerkner]

great! Merging now. Thank you!