In contemporary neuroscience, a key area of interest is dynamic effective connectivity, which is crucial for understanding the dynamic interactions and causal relationships between different brain regions. Dynamic effective connectivity can provide insights into how brain network interactions are altered in neurological disorders such as dyslexia. Time-varying vector autoregressive (TV-VAR) models have been employed to draw inferences for this purpose. However, their significant computational requirements pose challenges, since the number of parameters to be estimated increases quadratically with the number of time series. In this paper, we propose a computationally efficient Bayesian time-varying VAR approach. For dealing with large-dimensional time series, the proposed framework employs a tensor decomposition for the VAR coefficient matrices at different lags. Dynamically varying connectivity patterns are captured by assuming that at any given time only a subset of components in the tensor decomposition is active. Latent binary time series select the active components at each time via an innovative and parsimonious Ising model in the time-domain. Furthermore, we propose parsity-inducing priors to achieve global-local shrinkage of the VAR coefficients, determine automatically the rank of the tensor decomposition and guide the selection of the lags of the auto-regression. We show the performances of our model formulation via simulation studies and data from a real fMRI study involving a book reading experiment.

翻译：在现代神经科学中，动态有效连接性是一个关键研究领域，对于理解不同脑区之间的动态相互作用与因果关系至关重要。动态有效连接性能够揭示脑网络交互在诸如阅读障碍等神经系统疾病中的改变机制。时变向量自回归模型已被用于此类推断分析，但其巨大的计算需求构成了挑战，因为待估参数数量随时间序列数量呈二次方增长。本文提出一种计算高效的贝叶斯时变向量自回归方法。针对高维时间序列，该框架采用张量分解技术处理不同滞后阶数的向量自回归系数矩阵。通过假设张量分解中仅部分成分在任意时刻处于激活状态，模型能够捕捉动态变化的连接模式。潜在二元时间序列通过时域上创新的简约伊辛模型实现各时刻活跃成分的选择。此外，我们提出稀疏诱导先验来实现向量自回归系数的全局-局部收缩，自动确定张量分解的秩，并指导自回归滞后阶数的选择。通过仿真研究和真实功能磁共振成像数据（来自书籍阅读实验），我们验证了所提模型框架的性能表现。