torchcell.losses.distributional.coverage

coverage(pit: Tensor, alpha: float) → Tensor

Empirical coverage of the central alpha predictive interval, from PIT values.

An observation lies inside the central alpha interval \([\hat F^{-1}(\tfrac{1-\alpha}{2}),\ \hat F^{-1}(\tfrac{1+\alpha}{2})]\) exactly when its PIT lies in \([\tfrac{1-\alpha}{2}, \tfrac{1+\alpha}{2}]\), so coverage is a scalar read-off of the same transform rather than a second computation:

\[\mathrm{cov}_\alpha = \frac1N\sum \mathbf 1\!\left[\tfrac{1-\alpha}{2}\le \mathrm{PIT}\le \tfrac{1+\alpha}{2}\right].\]

Calibrated means \(\mathrm{cov}_\alpha \approx \alpha\). UNDER-coverage (\(<\alpha\)) is the U-shaped-PIT / overconfident case; OVER-coverage (\(>\alpha\)) is the n-shaped / sigma-collapse case.

Parameters:

• pit – PIT values, any shape (all entries are pooled).

• alpha – Nominal central interval mass in (0, 1), e.g. 0.8.

Returns:

Scalar coverage fraction.