Sparse-station temperature interpolation via Gaussian-process committees: an artificial intelligence evaluation of variance-inflation risk in national heat-health alert triggering

Abstract

Heat-health alert systems in data-sparse national settings depend on interpolated temperature fields whose uncertainty is rarely propagated into the trigger decision. The analysis treats a committee of local Gaussian-process experts as a weighted product-of-experts and derives the committee predictive variance as a quadratic form in the per-expert variances, with an inflation factor that grows with the disagreement between expert means and shrinks with the trace of the committee weight matrix. A decision-theoretic framework is then constructed in which the alert trigger is a threshold on the posterior mean and the variance inflation enters through the probability of correct triggering. Using NASA POWER monthly reanalysis for Harare over 2000-2023 (312 monthly observations, mean 18.914 C, standard deviation 3.107 C, warming trend 0.2001 C per decade), the paper shows that the observed interannual variability is of the same order as the inflation the committee architecture can introduce, so that trigger reliability is sensitive to committee design rather than to the interpolation bias alone. The contribution is a formal criterion for bounding committee-induced variance inflation in sparse-station interpolation and a demonstration that alert-trigger reliability should be evaluated against the inflation bound rather than against point-estimate accuracy.