Add relative efficiency function

[n-kall]

Summary

This would fix #280.

I am revisiting r_eff while implementing the weighted MCSE and ESS, which should take this into account (if draws are from MCMC).

I implemented relative_eff as ess_basic(x) / ndraws(x). This gives slightly lower (about 1%) results than loo::relative_eff. I guess due to the difference between loo:::rfun_ess and posterior::ess_basic

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/)

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 95.34%. Comparing base (9de9857) to head (34443df).

:exclamation: Current head 34443df differs from pull request most recent head 917c2e8. Consider uploading reports for the commit 917c2e8 to get more accurate results

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #354   +/-   ##
=======================================
  Coverage   95.33%   95.34%           
=======================================
  Files          50       50           
  Lines        3855     3863    +8     
=======================================
+ Hits         3675     3683    +8     
  Misses        180      180           

:umbrella: View full report in Codecov by Sentry.
:loudspeaker: Have feedback on the report? Share it here.

[github-actions[bot]]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 34443df2a75a1dbffedcf22d4fe03036e10cea24 is merged into master:

•   :ballot_box_with_check:as_draws_array: 142ms -> 141ms [-1.28%, +0.85%]
•   :rocket:as_draws_df: 66.5ms -> 65.4ms [-2.83%, -0.42%]
•   :rocket:as_draws_list: 162ms -> 160ms [-2.35%, -0.24%]
•   :rocket:as_draws_matrix: 66ms -> 64.8ms [-3.05%, -0.75%]
•   :ballot_box_with_check:as_draws_rvars: 80.8ms -> 80.5ms [-1.36%, +0.63%]
•   :ballot_box_with_check:summarise_draws_100_variables: 709ms -> 710ms [-0.11%, +0.41%]
•   :ballot_box_with_check:summarise_draws_10_variables: 109ms -> 109ms [-0.97%, +0.56%] Further explanation regarding interpretation and methodology can be found in the documentation.

[n-kall]

I changed this to a draft as I am now thinking about whether a single relative_eff function is the way to go. Perhaps there should be one for different quantities (like ESS) or none at all

[n-kall]

As a single r_eff function doesn't really make sense (it should be dependent on the quantity of interest), I will close this PR.