# Mean-dependent nonstationary spatial models

## TL;DR

This paper introduces a mean-dependent nonstationary spatial model that simplifies covariance estimation, improves prediction in certain cases, and includes a test for nonstationarity, demonstrated on Puerto Rico precipitation data.

## Contribution

The paper proposes a novel mean-dependent nonstationary spatial model that reduces complexity and enhances predictive performance compared to traditional models.

## Key findings

- Model improves predictions over stationary models in specific scenarios.
- Proposed approximation maintains predictive accuracy with lower computational cost.
- The nonstationarity test reliably detects nonstationary spatial data.

## Abstract

Nonstationarity is a major challenge in analyzing spatial data. For example, daily precipitation measurements may have increased variability and decreased spatial smoothness in areas with high mean rainfall. Common nonstationary covariance models introduce parameters specific to each location, giving a highly-parameterized model which is difficult to fit. We develop a nonstationary spatial model that uses the mean to determine the covariance in a region, resulting in a far simpler, albeit more specialized, model. We explore inferential and predictive properties of the model under various simulated data situations. We show that this model in certain circumstances improves predictions compared to a standard stationary spatial model. We further propose a computationally efficient approximation that has comparable predictive accuracy. We also develop a test for nonstationary data and show it reliably identifies nonstationarity. We apply these methods to daily precipitation in Puerto Rico.