Robust prediction of curves with spatial correlation: a Bayesian methodology applied to climate data

This work develops a hierarchical Bayesian methodology for predicting spatially correlated functional data by combining Universal Kriging–inspired decomposition with coherent probabilistic inference. The framework models each functional observation as a covariate-driven spatial trend plus a structured spatial random effect, both represented through basis-function expansions. A Matárn Gaussian process prior captures spatial dependence while a zero-mean Gaussian process ensures identifiability. Validation combines parameter-recovery and robustness studies; the latter tests performance under non-linear, nonadditive data generation violating model assumptions, revealing superior predictive performance relative to Universal Kriging for Functional Data (UKFD). Applied to hourly temperature data from 25 Mexico City stations across 2023, the model predicts annual temperature curves at four held-out locations, achieving 30–37% lower integrated squared error than UKFD at three sites. Formal calibration of 95% highest posterior density intervals reveals generally adequate coverage (81–100%), supporting evidence-based decision-making. Results underscore the impact of monitoring network density on spatial interpolation quality in environmental applications.