# Consistent Validation for Predictive Methods in Spatial Settings

arXiv: https://arxiv.org/abs/2402.03527 · HTML: https://mlsanity.com/paper/2402.03527/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2024.

## Built on by (most cited first, 2 of 2)

- [Smooth Sailing: Lipschitz-Driven Uncertainty Quantification for Spatial Association](https://mlsanity.com/paper/2502.06067/) (2025)
- [Wrong Model, Right Uncertainty: Spatial Associations for Discrete Data with Misspecification](https://mlsanity.com/paper/2509.01776/) (2025)

## Abstract (arXiv)

Spatial prediction tasks are key to weather forecasting, studying air pollution impacts, and other scientific endeavors. Determining how much to trust predictions made by statistical or physical methods is essential for the credibility of scientific conclusions. Unfortunately, classical approaches for validation fail to handle mismatch between locations available for validation and (test) locations where we want to make predictions. This mismatch is often not an instance of covariate shift (as commonly formalized) because the validation and test locations are fixed (e.g., on a grid or at select points) rather than i.i.d. from two distributions. In the present work, we formalize a check on validation methods: that they become arbitrarily accurate as validation data becomes arbitrarily dense. We show that classical and covariate-shift methods can fail this check. We propose a method that builds from existing ideas in the covariate-shift literature, but adapts them to the validation data at hand. We prove that our proposal passes our check. And we demonstrate its advantages empirically on simulated and real data.