How Much Can Sampling-Aware Uncertainty Buy? A Measurable Ceiling for Irregularly Sampled Time Series

A large line of work conditions predictive uncertainty on observation density: a model should be less certain where a channel is sampled too sparsely to resolve its variation. We measure what that idea is worth on four irregularly-sampled benchmarks and report three findings. Units decide the reading. The density–variance sign inversion that motivates such heads is present on PhysioNet's raw per-channel scales and absent under the z-scoring the baselines use ($-0.12$ to $+0.58$, every channel positive). And a selective-risk comparison on a per-channel standardized loss must rank by the variance in the loss's units: ranked by the raw $\sigma$, as our own boards were, our head appeared to beat a deep ensemble by $34\%$; aligned, the two are indistinguishable. A ceiling and a floor answer different questions. The tower property caps a variance head reading the observation set $S$ alone at $\mathrm{corr}({\hat{\sigma }}^2,e^2)\le \sqrt{s}$. We estimate the correlation ratio $s_T$ of a coarsening $T$ of $S$ — channel, horizon decile, density tercile — with a split-half statistic over whole sequences: on PhysioNet $\sqrt{s_T}$ is $0.120$ raw and $0.045$ z-scored. A cross-fitted $S$-only abstention rule lowers the normalised risk–coverage area by at least $0.377$ on PhysioNet and $0.208$ on USHCN for the mean of five fitted models, and a small ceiling does not bound this floor. Both are validated, including where they fail. Against a closed-form truth, interval coverage holds in heavy tails only because two biases cancel, falls to $84$–$88\%$ in light tails, and collapses when cells hold fewer than $50$ targets. On six forecasters' residuals, on three benchmark settings, the ceiling is similar while the floor depends on the forecaster. Our own density-conditioned head establishes no gain from its density input, and on PhysioNet the $S$-only lookup outranks its variance.