论文标题
空间索引功能时间序列的贝叶斯变更点估计值
Bayesian Changepoint Estimation for Spatially Indexed Functional Time Series
论文作者
论文摘要
我们建议在空间相关的功能时间序列中同时估算基于平均值的更改点，以同时估算贝叶斯分层模型。与以前在所有空间位置都假设共享更改点或忽略空间相关的方法不同，我们的方法将更改点视为空间过程。这使我们的模型可以尊重空间异质性和利用空间相关性以提高估计。我们的方法源自普遍存在的累积总和（CUSUM）统计量，该统计量主导了功能时间序列中的更改点检测。但是，我们没有直接搜索基于Cusum的过程的最大值，而是构建具有适当方差结构的空间相关的两件式线性模型，以一次定位所有更改点。提出的线性模型方法提高了我们方法在库司过程中变异性的鲁棒性，该方法与我们的空间相关模型相结合，改善了边缘附近的变更点估计。我们通过广泛的模拟研究证明，我们的方法在估计准确性和不确定性量化方面均优于现有的功能变更点估计值，这是在弱和强的空间相关性以及弱和强大变化信号下。最后，我们使用温度数据集和2019年冠状病毒病（COVID-19）研究证明了我们的方法。
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.
