Simultaneously detecting spatiotemporal changes with penalized Poisson regression models

In the realm of large-scale spatiotemporal data, abrupt changes are commonly occurring across both spatial and temporal domains. To address the concurrent challenges of detecting change points and identifying spatial clusters within spatiotemporal count data, an innovative method is introduced based on the Poisson regression model. The proposed method employs doubly fused penalization to unveil the underlying spatiotemporal change patterns. To efficiently estimate the model, an iterative shrinkage and threshold based algorithm is developed to minimize the doubly penalized likelihood function. The reliability and accuracy is confirmed by the statistical consistency properties. Furthermore, extensive numerical experiments are conducted to validate the theoretical findings, thereby highlighting the superior performance of the proposed method when compared to existing competitive approaches.