A calibrated flu posterior can still pick the wrong antiviral tier: a diagnostic scores decisions, not parameters

Whether an antiviral coverage tier is identifiable is a different property from whether the parameters are identifiable, and a posterior that passes conventional calibration checks can still leave the recommended tier undetermined. Earlier work on surveillance information content and on model sloppiness characterised reporting delay, under-reporting and practical non-identifiability, but did not ask whether the residual uncertainty changes the action. Across 192 synthetic grid cells the bounded neural posterior flipped the plug-in action in 26.7% of cells and the plug-in rule lost 11.7% of the oracle's value; parameter-layer non-identifiability showed no detectable relation to flip probability (Spearman +0.107, p=0.14, n=192).

Defining decision relevance as the projection of the loss gradient onto the sloppy subspace is misleading, whereas weighting by the variance of the decision margin separates sensitive from insensitive decisions. The geometric score failed its own scale-invariant control arm: under Fisher/Laplace geometry the main arm had a median of 0.0013 against a control of 0.0049, exceeding it in only 20.3% of cells, and under the neural posterior 0.0336 against 0.0967, or 11.5%. The variance-weighted score passed under two independent covariance sources: Fisher/Laplace at the true parameters gave 0.2996 against 0.1255 (78.1% of cells) and the neural posterior gave 0.2493 against 0.0498 (74.5%); the decision gradient is nearly orthogonal to the rho-i0 ridge, with a median absolute cosine of 0.036 under the bounded posterior.

The score applies directly to real surveillance and flags which seasons' model recommendations are least trustworthy. On synthetic seasons roughly half to two-thirds of cells had a decision margin no larger than its own uncertainty, against only 2.5% to 3.4% on real seasons. On 204 FluView region-seasons with a complete 6-week window across ten seasons from 2015-2016 to 2024-2025, widening the reporting-multiplier prior from one to three orders of magnitude raised the main arm from 0.476 to 0.733 while the control arm read 0.051, 0.0008 and 0.0049; six of the seven region-seasons failing the audit fall in 2022-2023.

The demonstrated setting is a six-parameter seasonal influenza SEIRS model with a single reported-case observation stream, a 192-cell synthetic design, and 204 FluView region-seasons from 2015-2016 to 2024-2025; the score is computed from the posterior a modelling team already holds, needs no additional data, and runs on a CPU.

The inverted relation in which higher counts accompany less identifiable decisions has a consistent sign across three synthetic routes and the real data, but no structural explanation is offered; the roughly twentyfold gap between synthetic and real seasons in the share of margins below their own uncertainty is explicitly left open. Sensitivity to the cost ratio lambda is stable within a threefold band, but the share of cells with margin signal-to-noise below 1 does not change monotonically with lambda.