Fix WIS: use w_median * |obs - median| on the array backends

[lucaluo925]

Summary

Fixes #140.

In scoringrules/core/interval/_score.py, changed WIS += w_median * median to WIS += w_median * B.abs(obs - median). Per Bracher et al. (2021) Eq. (3), this term is the weight multiplied by the absolute deviation between observation and median, not the median itself. The numba gufunc implementation was already correct; this change aligns the shared array backend path with it. Since _score.py is shared across numpy, jax, and torch, this fixes all three backends at once.

Also updated documentation: the docstring in _interval.py stated the default weight is w_k = 2/alpha_k, while the actual code uses alpha/2. The code was correct (consistent with the paper); only the docstring is updated.

Tests

The original test_weighted_interval_score passed the same obs value as both observation and median, so |obs - median| = 0. Both formulas yielded identical results, and the CI for all four backends remained green, hiding the bug. The test is updated to obs = 0.4, median = 0 so this term contributes meaningfully, with a comment explaining why observation and median must differ.

Added test_weighted_interval_score_median_term, which asserts directly against the closed-form solution from Eq. (3) in the paper, without relying on the approximation that "WIS approximates CRPS".

Validation

After reverting the source change, the two tests fail under the numpy backend (0.458 vs expected 0.338), while the numba backend still passes — confirming the bug only affects non-numba paths. After restoring the fix, all 6 tests in tests/test_interval.py pass. Environment: Python 3.14, numpy 2.5.3, numba 0.67.0.

jax and torch are not installed in my environment, so I could only exercise the numpy and numba backends locally; CI will be the first run covering all four.

AI note

The code changes and tests were written with assistance from an AI assistant. I reproduced the bug locally, ran the tests, and verified that the tests fail when the fix is reverted.

Checklist

• Tests pass across all backends — uv sync --all-extras --dev then uv run pytest tests/ (exercises every installed backend: numpy, numba, jax, torch)
• New/changed numerics touch both the array-API and numba paths where applicable
• Docs / docstrings updated if public behavior changed
• A release-note label is applied (breaking, enhancement, bug, backend, documentation, or ci)

(I can't apply labels myself — bug looks like the right one here.)