# Basis-Function Models in Spatial Statistics

arXiv: https://arxiv.org/abs/2202.03660 · HTML: https://mlsanity.com/paper/2202.03660/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2022.

## Built on by (most cited first, 9 of 9)

- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Fusing Climate Data Products using a Spatially Varying Autoencoder](https://mlsanity.com/paper/2403.07822/) (2024)
- [Probabilistic Spatiotemporal Modeling of Day-Ahead Wind Power Generation with Input-Warped Gaussian Processes](https://mlsanity.com/paper/2409.16308/) (2024)
- [Positional Encoder Graph Quantile Neural Networks for Geographic Data](https://mlsanity.com/paper/2409.18865/) (2024)
- [Bayesian Kernelized Tensor Factorization as Surrogate for Bayesian Optimization](https://mlsanity.com/paper/2302.14510/) (2023)
- [Logistic-beta processes for dependent random probabilities with beta marginals](https://mlsanity.com/paper/2402.07048/) (2024)
- [A Framework for Nonstationary Gaussian Processes with Neural Network Parameters](https://mlsanity.com/paper/2507.12262/) (2025)
- [Spatiodynamic inference using vision-based generative modelling](https://mlsanity.com/paper/2507.22256/) (2025)
- [Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices](https://mlsanity.com/paper/2609.30348/) (2026)

## Abstract (arXiv)

Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation from a probability model that encodes the dependence through both fixed effects and random effects, where randomness is manifest in the underlying spatial process and in the noisy, incomplete, measurement process. The focus of this review article is on the use of basis functions to provide an extremely flexible and computationally efficient way to model spatial processes that are possibly highly non-stationary. Several examples of basis-function models are provided to illustrate how they are used in Gaussian, non-Gaussian, multivariate, and spatio-temporal settings, with applications in geophysics. Our aim is to emphasise the versatility of these spatial statistical models and to demonstrate that they are now centre-stage in a number of application domains. The review concludes with a discussion and illustration of software currently available to fit spatial-basis-function models and implement spatial-statistical prediction.