大规模球面时空数据中的可扩展突变点检测
Scalable Changepoint Detection for Large Spatiotemporal Data on the Sphere
AI总结：
本文提出了一种基于多项式概率模型和高斯过程的贝叶斯框架，用于高效检测大规模球面时空数据中的突变点，通过SPDE和球面谐波变换实现计算效率与精度的平衡。
摘要：
我们提出了一种新的贝叶斯框架，用于大规模球面时空数据中的突变点检测，广泛应用于环境和气候科学。我们的方法利用多项式概率模型（MPM）与潜在高斯过程，将突变点建模为空间依赖的分类变量，有效捕捉球面上复杂的空间相关结构。为处理全球数据集固有的高维性，我们利用随机偏微分方程（SPDE）和球面谐波变换，实现高效的表示和可扩展推断，大幅减少计算负担同时保持高精度。通过广泛的模拟研究，我们展示了所提出方法在突变点估计中的效率和鲁棒性，以及通过结合MPM和截断谱表示的潜在过程所实现的显著计算优势。最后，我们将方法应用于全球气溶胶光学深度数据，成功识别了与重大大气事件相关的突变点。
英文摘要：
We propose a novel Bayesian framework for changepoint detection in large-scale spherical spatiotemporal data, with broad applicability in environmental and climate sciences. Our approach models changepoints as spatially dependent categorical variables using a multinomial probit model (MPM) with a latent Gaussian process, effectively capturing complex spatial correlation structures on the sphere. To handle the high dimensionality inherent in global datasets, we leverage stochastic partial differential equations (SPDE) and spherical harmonic transformations for efficient representation and scalable inference, drastically reducing computational burden while maintaining high accuracy. Through extensive simulation studies, we demonstrate the efficiency and robustness of the proposed method for changepoint estimation, as well as the significant computational gains achieved through the combined use of the MPM and truncated spectral representations of latent processes. Finally, we apply our method to global aerosol optical depth data, successfully identifying changepoints associated with a major atmospheric event.
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