This manuscript puts forward novel practicable spatiotemporal Bayesian factor analysis frameworks computationally feasible for moderate to large data. Our models exhibit significantly enhanced computational scalability and storage efficiency, deliver high overall modeling performances, and possess powerful inferential capabilities for adequately predicting outcomes at future time points or new spatial locations and satisfactorily clustering spatial locations into regions with similar temporal trajectories, a frequently encountered crucial task. We integrate on top of a baseline separable factor model with temporally dependent latent factors and spatially dependent factor loadings under a probit stick breaking process (PSBP) prior a new slice sampling algorithm that permits unknown varying numbers of spatial mixture components across all factors and guarantees them to be non-increasing through the MCMC iterations, thus considerably enhancing model flexibility, efficiency, and scalability. We further introduce a novel spatial latent nearest-neighbor Gaussian process (NNGP) prior and new sequential updating algorithms for the spatially varying latent variables in the PSBP prior, thereby attaining high spatial scalability. The markedly accelerated posterior sampling and spatial prediction as well as the great modeling and inferential performances of our models are substantiated by our simulation experiments.

翻译：本文提出了适用于中大规模数据的实用化时空贝叶斯因子分析框架。我们的模型在计算可扩展性与存储效率方面显著提升，具备优异的整体建模性能，并拥有强大的推断能力，能够准确预测未来时间点或新空间位置的结果，同时有效将空间位置聚类为具有相似时间轨迹的区域——这是实际应用中常见的关键任务。我们在基础可分离因子模型（具有时间相关的潜在因子与空间相关的因子载荷）之上，通过概率比随机过程（PSBP）先验，整合了一种新的切片采样算法。该算法允许各因子的空间混合成分数量未知且可变，并保证其在MCMC迭代过程中非递增，从而显著增强了模型的灵活性、效率与可扩展性。我们进一步引入了新颖的空间潜在最近邻高斯过程（NNGP）先验，并为PSBP先验中空间变化的潜在变量设计了新的序贯更新算法，从而实现了高度的空间可扩展性。通过仿真实验，我们验证了所提模型在显著加速后验采样与空间预测方面的优势，以及其卓越的建模与推断性能。