Valid Model-Free Spatial Prediction

Predicting the response at an unobserved location is afundamental problem in spatial statistics. Giventhe difficulty in modeling spatial dependence, especially in nonstationary cases, model-based predictionintervals are at risk of misspecification bias that can negatively affect their validity. Here we present a newapproach for model-free nonparametric spatial prediction based on theconformal predictionmachinery.Our key observation is that spatial data can be treated as exactly or approximately exchangeable in awide range of settings. In particular, under an infill asymptotic regime, we prove that the response valuesare, in a certain sense, locally approximately exchangeable for a broad class of spatial processes, and wedevelop a local spatial conformal prediction algorithm that yields valid prediction intervals without strongmodel assumptions like stationarity. Numerical exampleswith both real and simulated data confirm that theproposed conformal prediction intervals are valid and generally more efficient than existing model-basedprocedures for large datasets across a rangeof nonstationary and non-Gaussian settings.