We propose a Bayesian hierarchical model to simultaneously estimate mean based changepoints in spatially correlated functional time series. Unlike previous methods that assume a shared changepoint at all spatial locations or ignore spatial correlation, our method treats changepoints as a spatial process. This allows our model to respect spatial heterogeneity and exploit spatial correlations to improve estimation. Our method is derived from the ubiquitous cumulative sum (CUSUM) statistic that dominates changepoint detection in functional time series. However, instead of directly searching for the maximum of the CUSUM based processes, we build spatially correlated two-piece linear models with appropriate variance structure to locate all changepoints at once. The proposed linear model approach increases the robustness of our method to variability in the CUSUM process, which, combined with our spatial correlation model, improves changepoint estimation near the edges. We demonstrate through extensive simulation studies that our method outperforms existing functional changepoint estimators in terms of both estimation accuracy and uncertainty quantification, under either weak and strong spatial correlation, and weak and strong change signals. Finally, we demonstrate our method using a temperature data set and a coronavirus disease 2019 (COVID-19) study.
翻译:我们提出了一个贝叶斯等级模型,以同时估算空间相关功能时间序列中以平均为基础的平均变化点。我们的方法与以前假定所有空间位置都有一个共同变化点或忽略空间相关性的方法不同,我们的方法将变化点视为空间过程。这使我们的模型能够尊重空间异质性并利用空间相关关系来改进估计。我们的方法来自支配功能时间序列中变化点检测的无处不在的累积和(CUSUUM)统计。然而,我们不直接寻找基于 CUSUM 进程的最大数量,而是建立具有适当差异结构的空间相关两件双件线性模型,以同时定位所有变化点。拟议线性模型方法提高了我们在CUSUM进程中变化点的方法的稳健性,该模型与我们的空间相关模型一起,改进了边缘附近的变化点估算。我们通过广泛的模拟研究发现,我们的方法在估算精确性和不确定性的量化方面,在弱和强的空间相关性下,以及弱和强的改变信号下,都比现有的功能性点估计标准。最后,我们用温度数据设置和CO-19 研究来展示我们的方法。