Mixed-Stationary Gaussian Process for Flexible Non-Stationary Modeling of Spatial Outcomes

TL;DR

This paper introduces a flexible non-stationary Gaussian process model for spatial data that assigns individual stationarity parameters to each location, using a mixture model to balance flexibility and computational tractability.

Contribution

It develops a novel non-stationary GP framework with location-specific parameters and a non-parametric mixture approach to improve modeling flexibility and prediction efficiency.

Findings

Model performs well on simulated data.

Effective on large-scale temperature datasets.

Theoretical properties are established.

Abstract

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the latter suffers from intractable computation and can lead to overfitting. Taking the instantaneous stationarity idea, we construct a non-stationary GP with the stationarity parameter individually set at each location. Then we utilize the non-parametric mixture model to reduce the effective number of unique parameters. Different from a simple mixture of independent GPs, the mixture in stationarity allows the components to be spatial correlated, leading to improved prediction efficiency. Theoretical properties are examined and a linearly scalable algorithm is provided. The application is shown through several simulated scenarios as well as the massive spatiotemporally correlated temperature data.