# Regression-based covariance functions for nonstationary spatial modeling

arXiv: https://arxiv.org/abs/1410.1494 · HTML: https://mlsanity.com/paper/1410.1494/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2014.

## Built on by (most cited first, 5 of 5)

- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Advanced Stationary and Non-Stationary Kernel Designs for Domain-Aware Gaussian Processes](https://mlsanity.com/paper/2102.03432/) (2021)
- [Compactly-supported nonstationary kernels for computing exact Gaussian processes on big data](https://mlsanity.com/paper/2411.05869/) (2024)
- [A class of modular and flexible covariate-based covariance functions for nonstationary spatial modeling](https://mlsanity.com/paper/2410.16716/) (2024)
- [GGMPs: Generalized Gaussian Mixture Processes](https://mlsanity.com/paper/2603.10442/) (2026)

## Abstract (arXiv)

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of models for continuously-indexed spatial data is the covariance function, which is traditionally assumed to belong to a parametric class of stationary models. However, stationarity is rarely a realistic assumption. Alternative methods which more appropriately model the nonstationarity present in environmental processes often involve high-dimensional parameter spaces, which lead to difficulties in model fitting and interpretability. To overcome this issue, we build on the growing literature of covariate-driven nonstationary spatial modeling. Using process convolution techniques, we propose a Bayesian model for continuously-indexed spatial data based on a flexible parametric covariance regression structure for a convolution-kernel covariance matrix. The resulting model is a parsimonious representation of the kernel process, and we explore properties of the implied model, including a description of the resulting nonstationary covariance function and the interpretational benefits in the kernel parameters. Furthermore, we demonstrate that our model provides a practical compromise between stationary and highly parameterized nonstationary spatial covariance functions that do not perform well in practice. We illustrate our approach through an analysis of annual precipitation data.