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.