# Non-Stationary Spatial Modeling

arXiv: https://arxiv.org/abs/2212.08043 · HTML: https://mlsanity.com/paper/2212.08043/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2022.

## Built on by (most cited first, 13 of 13)

- [A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processes](https://mlsanity.com/paper/2309.10068/) (2023)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [A class of modular and flexible covariate-based covariance functions for nonstationary spatial modeling](https://mlsanity.com/paper/2410.16716/) (2024)
- [Bayesian Optimization over Bounded Domains with the Beta Product Kernel](https://mlsanity.com/paper/2506.16316/) (2025)
- [gp2Scale: A Class of Compactly Supported Non-Stationary Kernels and Distributed Computing for Exact Gaussian Processes on 10 Million Data Points](https://mlsanity.com/paper/2512.06143/) (2025)
- [Mind the Jumps: A Scalable Robust Local Gaussian Process for Multidimensional Response Surfaces with Discontinuities](https://mlsanity.com/paper/2512.12574/) (2025)
- [A New Reliable & Parsimonious Learning Strategy Comprising Two Layers of Gaussian Processes, to Address Inhomogeneous Empirical Correlation Structures](https://mlsanity.com/paper/2404.12478/) (2024)
- [A Framework for Nonstationary Gaussian Processes with Neural Network Parameters](https://mlsanity.com/paper/2507.12262/) (2025)
- [Modeling nonstationary spatial processes with normalizing flows](https://mlsanity.com/paper/2509.12884/) (2025)
- [Regime-Adaptive Bayesian Optimization via Dirichlet Process Mixtures of Gaussian Processes](https://mlsanity.com/paper/2601.20043/) (2026)
- [Nonparametric Bayesian Optimization for General Rewards](https://mlsanity.com/paper/2602.07411/) (2026)
- [Regular Fourier Features for Nonstationary Gaussian Processes](https://mlsanity.com/paper/2602.23006/) (2026)
- [Predicting Covariate-Driven Spatial Deformation for Nonstationary Gaussian Processes](https://mlsanity.com/paper/2604.27280/) (2026)

## Abstract (arXiv)

Standard geostatistical models assume stationarity and rely on a variogram model to account for the spatial dependence in the observed data. In some instances, this assumption that the spatial dependence structure is constant throughout the sampling region is clearly violated. We present a spatial model which allows the spatial dependence structure to vary as a function of location. Unlike previous formulations which do not account for uncertainty in the specification of this non-stationarity (eg. Sampson and Guttorp (1992)), we develop a hierarchical model which can incorporate this uncertainty in the resulting inference. The non-stationary spatial dependence is explained through a constructive "process-convolution" approach, which ensures that the resulting covariance structure is valid. We apply this method to an example in toxic waste remediation.