Mixed-Stationary Gaussian Process for Flexible Non-Stationary Modeling of Spatial Outcomes
This provides a flexible method for spatial statisticians to handle non-stationary outcomes, though it is incremental by building on existing instantaneous stationarity ideas.
The paper tackles the challenge of modeling non-stationary spatial data with Gaussian processes by introducing a mixed-stationary GP that assigns individual stationarity parameters to each location and uses a non-parametric mixture to reduce parameters, achieving improved prediction efficiency as demonstrated on simulated and temperature data.
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.