Cause and mitigation of spatially variable calibration efficacy

Determine the causes of the variable efficacy of post hoc calibration across sub-regions of the dark-energy equation-of-state and total-matter-density parameter space, and develop methods that mitigate these inconsistencies.

Background

The post hoc calibration rescales the population-level likelihood ratio using a single global correction derived over the full parameter space. Although this improves calibration across the entire test region, its performance varies substantially among individual sub-regions: some remain overconfident in one cosmological parameter, while others become underconfident or show structured coverage errors. The authors explicitly identify the unexplained source of this variation and its mitigation as the next major research problem for making the method reliable throughout the parameter space.

References

Nonetheless, this is still on-average near-pivotal. It must be stressed that this leaves open a gap for severely non-pivotal behaviour at some parameter values to be traded off against consequently improved behaviour at others. This is particularly possible at low-probability parameter values, where very poor calibration may nonetheless have a very small impact on the loss.

— Likelihood-free inference with nuisance parameters through normalizing flows  (2609.10534 - Assheton, 9 Sep 2026) in Section 5.2.1, “Suitability of KL optimization”

We have not yet uncovered the cause of variable efficacy of the calibration from Sub-Region to Sub-Region or what allows the calibration to succeed for the Entire Test Region, while not consistently successfully across the Sub-Regions. This is the next major step for future studies.

— Strong Lensing Cosmology with Population-level Calibrated Neural Ratio Estimation  (2608.23534 - Jarugula et al., 24 Aug 2026) in Section 6.3, Sub-Region calibration consistency; Section 7, Conclusion