A Bayesian Spatiotemporal Functional Model for Data With Block Structure and Repeated Measures

ABSTRACT The analysis of spatiotemporal data is fundamental across multiple scientific disciplines, particularly in assessing the behavior of climate effects over space and time. A key challenge in this area is effectively capturing recurring climate phenomena, such as El Niño/La Niña (ENSO) phases, which induce prolonged periods of similar weather patterns across affected regions. To address this, our study introduces a novel spatiotemporal regression model that explicitly incorporates block structures representing these recurring climate effects. These blocks accommodate ENSO phases and manage the within‐block correlations and shared characteristics, enhancing the model's ability to capture the influence of such phenomena on precipitation variability. The model further integrates functional predictors of both fixed and random nature, along with spatial covariance modeled via the Matérn class, to accommodate complex spatial, temporal, and block‐related structures. Motivated by a monthly precipitation dataset from meteorological stations in Goiás State, Brazil, spanning 21 years (1980–2001), our approach assigns spatial effects to individual stations, temporal effects to months, blocks to ENSO phases, and repeated measures to years within those blocks. The results from simulation studies demonstrate the model's robustness and effectiveness, providing deeper insight into how recurring climate effects like ENSO impact rainfall patterns. This framework represents a significant methodological advancement in spatiotemporal modeling, highlighting the importance of explicitly modeling and estimating the effects of recurrent climate phenomena through block structures.