Hierarchical Spatio‐Temporal Model Under t$$ t $$‐Process With Application

Gaussian process has been widely used in spatio‐temporal models to analyze and reveal the underlying correlation of spatio‐temporal data. Nevertheless, inferences drawn from Gaussian process‐based models can be highly sensitive to outliers or distributional misspecifications. To enhance robustness, we propose a robust hierarchical spatio‐temporal model based on Student‐t$$ t $$ process framework to enable reliable inferences under data contamination. The proposed model employs two independent t$$ t $$‐processes to respectively describe the latent spatial random effects and random errors, thereby ensuring robust inferences against various types of outliers. A variational Expectation‐Maximization algorithm is developed for efficient parameter estimation and prediction. Simulation studies demonstrate that the proposed model delivers reliable and accurate results even when the data are contaminated by substantial outliers. The practical usefulness of the model is further illustrated through an application to PM2.5$$ {\mathrm{PM}}_{2.5} $$ concentration data, highlighting its effectiveness in robust spatio‐temporal inference.