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

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.