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可实用化时空贝叶斯因子分析框架。所构建的模型在计算可扩展性与存储效率方面具有显著提升，能够实现整体建模性能的最优化，同时具备强大的推断能力，可准确预测未来时间点或新空间位置的输出结果，并有效完成将空间位置按相似时间轨迹进行聚类的关键任务。我们在基准可分离因子模型基础上，整合了具有时间依赖性潜在因子与空间依赖性因子载荷（采用probit stick breaking过程先验），并引入新型切片采样算法。该算法允许所有因子对应的空间混合成分数量未知且随MCMC迭代呈非递增变化，从而显著增强模型的灵活性、效率与可扩展性。进一步地，我们提出了适用于PSBP先验中空间变参数的新型空间潜在最近邻高斯过程（NNGP）先验与序贯更新算法，由此实现高空间可扩展性。仿真实验验证了模型在后验采样与空间预测速度上的显著加速，以及其卓越的建模与推断性能。