Weighted diagnostics

[n-kall]

Summary

Adds weighted ESS, MCSE and Pareto diagnostics.

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]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 77cdf1a is merged into rvar_weights:

•   :rocket:as_draws_array: 141ms -> 139ms [-2.13%, -0.83%]
•   :ballot_box_with_check:as_draws_df: 64.8ms -> 65.1ms [-1.67%, +2.43%]
•   :ballot_box_with_check:as_draws_list: 158ms -> 158ms [-0.74%, +1.11%]
•   :ballot_box_with_check:as_draws_matrix: 62.7ms -> 63.4ms [-0.79%, +2.97%]
•   :ballot_box_with_check:as_draws_rvars: 80.5ms -> 81.6ms [-0.13%, +2.77%]
•   :ballot_box_with_check:summarise_draws_100_variables: 709ms -> 710ms [-0.24%, +0.47%]
•   :ballot_box_with_check:summarise_draws_10_variables: 111ms -> 111ms [-1.44%, +0.6%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[paul-buerkner]

Thank you! @avehtari would you have time to review this PR?

[n-kall]

I should still add some documentation, but I think the core functionality is there (plus tests)

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if d56a5c9 is merged into rvar_weights:

•   :rocket:as_draws_array: 151ms -> 149ms [-1.92%, -0.49%]
• ❗🐌as_draws_df: 72.8ms -> 73.7ms [+0.27%, +2.25%]
•   :ballot_box_with_check:as_draws_list: 168ms -> 168ms [-0.58%, +0.7%]
•   :ballot_box_with_check:as_draws_matrix: 67.8ms -> 67.3ms [-1.9%, +0.47%]
•   :ballot_box_with_check:as_draws_rvars: 84.5ms -> 84.2ms [-1.43%, +0.69%]
•   :ballot_box_with_check:summarise_draws_100_variables: 719ms -> 721ms [-0.14%, +0.53%]
•   :ballot_box_with_check:summarise_draws_10_variables: 116ms -> 116ms [-0.98%, +0.35%]
  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 1079cef is merged into rvar_weights:

• ✔️as_draws_array: 137ms -> 137ms [-0.89%, +0.54%]
• ✔️as_draws_df: 60.9ms -> 61.2ms [-1.14%, +2.31%]
• ❗🐌as_draws_list: 156ms -> 157ms [+0.53%, +1.79%]
• ✔️as_draws_matrix: 60ms -> 59.4ms [-2.16%, +0.01%]
• ✔️as_draws_rvars: 82ms -> 82.5ms [-0.5%, +1.7%]
• ❗🐌summarise_draws_100_variables: 707ms -> 741ms [+4.44%, +5.01%]
• ✔️summarise_draws_10_variables: 110ms -> 111ms [-0.2%, +1.03%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[n-kall]

I think this can be merged into the weighted rvars branch, as @avehtari and I went through and reviewed this some time ago

[paul-buerkner]

Thanks. Merging now.