Valid Model-Free Spatial Prediction

Abstract

Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in nonstationary cases, model-based prediction intervals are at risk of misspecification bias that can negatively affect their validity. Here we present a new approach for model-free nonparametric spatial prediction based on the conformal prediction machinery. Our key observation is that spatial data can be treated as exactly or approximately exchangeable in a wide range of settings. In particular, under an infill asymptotic regime, we prove that the response values are, in a certain sense, locally approximately exchangeable for a broad class of spatial processes, and we develop a local spatial conformal prediction algorithm that yields valid prediction intervals without strong model assumptions like stationarity. Numerical examples with both real and simulated data confirm that the proposed conformal prediction intervals are valid and generally more efficient than existing model-based procedures for large datasets across a range of nonstationary and non-Gaussian settings.

Keywords:

• Conformal prediction
• Gaussian process
• Kriging
• Nonstationary
• Plausibility

Acknowledgments

The authors thank the reviewers for their thoughtful and critical comments on a previous version of the manuscript. HM (DMS–1638521) and RM (DMS–1811802) are supported by the National Science Foundation. BJR is supported by the National Institutes of Health (R01ES031651 and R01ES027892) and King Abdullah University of Science and Technology (3800.2).

Additional information

Funding

HM (DMS–1638521) and RM (DMS–1811802) are supported by the National Science Foundation. BJR is supported by the National Institutes of Health (R01ES031651 and R01ES027892) and King Abdullah University of Science and Technology (3800.2).