LOO refactoring and adding pred_measure feature

[florence-bockting]

Fixes #281

This PR is work in progress and the description will be refined over time.

Description

This PR is a larger project with the aim to refactor the loo package and to add new features related to a new pred_measure family.

In the course of refactoring this PR aims to address also the following PRs:

• Fixes (loo_)(s)crps could ask for only one argument with predictions #223: (s)crps should require only one ypred argument as input.
• Fixes loo_compare for crps and loo_crps #220: implement crps for insample/loo/kfold/test and have an interface to loo_compare
• Fixes loo_predictive_metric and loo_crps could accept psis objects to reduce computation #213: (s)crps should accept pre-computed psis_object besides internal computation of psis_object.
• Fixes Add R2 #201: Support custom measures and provide R2 as built-in measure.
• Fixes user defined loss/utility functions #135: Support of custom measures (i.e., loss/utility functions)
• Fixes loo.function should not require a r_eff argument #106; Fixes Change n_eff to ESS #192: Handling of r_eff in loo.function
• Fixes Improve warnings and messages behavior #353: Improve handling of warnings and messages

How to navigate this PR

As this is a large, long-running PR it might help to first read through the supporting documents that explain the design, scope, and current status:

• developer-notes.md: The central reference for this project: current status, open tasks, outstanding design decisions, and known blockers. Start here.
• pred_measure-formulas.Rmd: An overview of all supported scores and metrics, including their mathematical definitions.
• pred_measure-family.Rmd: A conceptual introduction to the new pred_measure family and its intended usage.

Acknowledgements

This work builds on an initial prototype of the new pred_measure feature implemented by @VisruthSK under guidance from @jgabry (see VisruthSK/loo-sandbox).

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 7649d9c is merged into master:

• ✔️loo_function: 1.75s -> 1.75s [-0.29%, +0.62%]
• ✔️loo_matrix: 1.32s -> 1.32s [-0.7%, +0.4%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[florence-bockting]

Linking here to Issue #179 as it seems to be about loo scores. We should see whether it is still relevant and can be implemented within loo refactoring.

• Add issue Calibration/Refinement Decomposition of LOO Scores #179 to PR description text if we can address it.

[florence-bockting]

There is an open issue requesting a subset() method for psis objects #343 and an (unrelated) open PR #110. Might be worth considering whether we can address this as well in this refactoring PR. If yes, we should

• close PR Subsetting psis objects #110 with link to this PR and also
• mark issue Feature Request: public subset() method for psis objects #343 as fixed in the description text of this PR.