Rename diagnostics$n_eff to diagnostics$ess with backward-compatible deprecation

[ishaan-arora-1]

Hi! This PR implements the n_eff → ess rename discussed in #192, following the approach @jgabry outlined in the comments there.

What this does

The diagnostics list in loo/psis/tis/sis objects now uses ess (effective sample size) as the canonical name instead of n_eff, aligning with the terminology used by the posterior package and the updated Rhat paper.

Implementation approach

I went with the phased deprecation strategy from the issue discussion:

1. New loo_diagnostics S3 class — the diagnostics list now has its own class, which was a prerequisite @jgabry identified for being able to define custom extractors.

2. Both slots present — the constructor loo_diagnostics(pareto_k, ess, r_eff) stores both ess and n_eff (set to the same value), so existing code that accesses n_eff by position or via unclass() won't break immediately.

3. Deprecation warnings on n_eff access — custom $, [[, and [ methods on loo_diagnostics warn when n_eff is accessed, suggesting ess instead. This follows the exact same pattern used for the deprecated estimate extractors on loo objects (the $.loo / [[.loo / [.loo methods in loo.R).

4. Sync on assignment — custom $<- and [[<- methods ensure that assigning to either ess or n_eff keeps both in sync, so code that does things like loo$diagnostics$n_eff[i] <- value during moment matching still works correctly.

5. psis_n_eff_values() updated — now reads from ess first, falling back to n_eff for backward compatibility with older serialized objects.

6. Internal column rename — pareto_k_table now uses "Min. ESS" as the internal column name (the print method was already displaying it as "Min. ESS" since use new k threshold #235, but the actual matrix column was still "Min. n_eff").

Files changed

• R/diagnostics.R — new class, constructor, extractor methods, updated psis_n_eff_values and pareto_k_table
• R/importance_sampling.R — use loo_diagnostics() constructor
• R/loo.R — use loo_diagnostics() in loo.function and list2importance_sampling
• R/loo_approximate_posterior.R — same
• R/loo_moment_matching.R — use ess internally
• R/loo_subsample.R — reconstruct diagnostics properly during subsample operations
• R/psis.R, R/tis.R, R/sis.R — updated roxygen docs
• NAMESPACE — registered new S3 methods
• Tests updated across 7 test files
• NEWS.md entry added

Note on snapshots

The serialized snapshot in tests/testthat/_snaps/psis.md for "psis results haven't changed" will need to be regenerated (via testthat::snapshot_accept()) since the diagnostics structure now includes the ess slot and the loo_diagnostics class. I didn't want to blindly accept snapshots without running the full test suite locally, so I left that for the CI / reviewer to handle.

What I didn't change

Per the issue discussion, I left r_eff as-is — it's conceptually different (relative MCMC efficiency) and doesn't need renaming.

Fixes #192

[codecov-commenter]

Codecov Report

❌ Patch coverage is 92.59259% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 92.71%. Comparing base (2883f25) to head (74ab82d).

Files with missing lines	Patch %	Lines
R/diagnostics.R	87.50%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #327      +/-   ##
==========================================
- Coverage   92.78%   92.71%   -0.07%     
==========================================
  Files          31       31              
  Lines        2992     3048      +56     
==========================================
+ Hits         2776     2826      +50     
- Misses        216      222       +6     

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