Weighted model calibration and its limits

Abstract

In spatial data analysis, accounting for spatial autocorrelation is crucial for accurate model estimation and prediction. While process-based models are often used to simulate physical mechanisms driving spatial patterns, they are typically unconditioned to observed data and computationally expensive to calibrate with spatial structure directly. This study evaluates a spatial weighting scheme proposed by Nguyen et al. (2025) that integrates spatial conditional information into cost functions for model calibration. Using the Meuse dataset, we conducted simulations under varying levels of spatial noise and compared the performance of a spatially weighted linear model to a conventional unweighted model. Results demonstrate that the weighted model consistently achieves better parameter coverage and prediction accuracy, particularly in the presence of moderate to high spatial dependence. By downweighting redundant information from spatially correlated observations, the method improves inference and tightens prediction intervals. These findings highlight the utility of spatially weighted cost functions not only for geostatistical regression but also as a scalable solution for calibrating process-based models, enabling them to account for spatial dependence without embedding it directly into the simulation.