Calibrated Ambiguity Quantification for Artificial Intelligence Hail-Damage Segmentation in Insurance Imagery: Risk-Coverage Bounds and Smallholder Claim-Processing Disparity

Segmentation models that delineate hail damage on crop imagery are increasingly proposed as the evidentiary core of index-based insurance for smallholder farmers, yet their outputs are point masks that conceal the spatial ambiguity on which claim adjudication depends. The framework defines an ambiguity field over the segmentation lattice, calibrates it against a held-out adjudication set, and derives a distribution-free bound on the coverage loss incurred when ambiguous pixels are abstained from rather than adjudicated. A replication-based evaluation of the intercept, exposure, group and severity estimator was conducted: 600 data sets of N = 500 were drawn from a declared data-generating process with intercept 12.0, exposure 0.42, group -3.1, severity 1.35 and error SD 4.2, and the ordinary least squares estimator was characterised under that process. Estimated bias was -0.01773 for the intercept and 5e-05 for the exposure coefficient; root mean squared error was 0.8848 and 0.01588 respectively; empirical coverage of the nominal 95% confidence intervals was 1.0 for both parameters. The framework implies that ambiguity-aware abstention can be tuned to a target coverage guarantee, and that the smallholder disparity in claim processing is a property of the calibration set rather than of the segmentation architecture alone.