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新型实用时空贝叶斯因子分析框架。我们的模型在计算可扩展性和存储效率方面表现出显著提升，具备优异的整体建模性能，并拥有强大的推断能力，能够有效预测未来时间点或新空间位置的结果，同时将空间位置按相似时间轨迹聚类到区域中——这是一项频繁出现的关键任务。我们在基准可分离因子模型基础上，集成时间相关潜在因子和空间相关因子载荷（采用probit stick breaking process (PSBP)先验），引入了一种新的切片采样算法，该算法允许所有因子的空间混合成分数量未知且动态变化，并通过MCMC迭代确保其非递增，从而大幅增强模型灵活性、效率和可扩展性。我们进一步提出了新型空间潜在最近邻高斯过程（NNGP）先验，以及针对PSBP先验中空间变化潜在变量的序列更新算法，从而实现了高度的空间可扩展性。仿真实验证实了我们的模型在显著加速后验采样和空间预测方面的表现，以及其卓越的建模与推断性能。