Conformal prediction for spatial data with GAM-trend adjustment

Abstract

Reliable uncertainty quantification for spatial prediction remains a central challenge due to the sensitivity of classical geostatistical methods, particularly kriging, to assumptions of stationarity, Gaussianity, and correctly specified covariance models.This study presents a practical three-step framework that integrates model-based detrending with distribution-free calibration to construct robust prediction intervals for spatial data.First, largescale spatial trends are removed using a generalized additive model (GAM).Second, residual ordinary kriging (OK) captures medium-scale spatial dependence and provides location-specific standard errors.Third, split conformal prediction (CP) is applied to the doubly detrended residuals to guarantee finite-sample coverage.Two types of conformity scores are considered: the absolute residual and a variance-scaled version normalized by the kriging standard error.Spatial block partitioning mitigates calibration-test dependence, while diagnostics such as Moran's I and variance homogeneity tests assess approximate exchangeability.Application to the meuse dataset demonstrates that the proposed approach attains coverage near the nominal level under random splits and slightly conservative coverage under spatial blocking, while maintaining competitive average interval length compared with Gaussian plug-in intervals.The framework provides a robust, model-agnostic alternative for spatial uncertainty quantification when traditional parametric assumptions are unreliable, offering practical utility for environmental and geoscientific applications.