带累积收缩先验的离散自回归切换过程用于时间序列数据的图模型
Discrete Autoregressive Switching Processes with Cumulative Shrinkage Priors for Graphical Modeling of Time Series Data
AI总结：
针对多元时间序列的稀疏高斯图建模问题，提出结合隐藏离散自回归过程、图马蹄形先验和累积收缩先验的贝叶斯方法，可估计状态数与滞后数，经模拟验证性能，还能用于基于fMRI数据的动态脑连接估计。
摘要：
我们提出一种灵活的贝叶斯方法，用于多元时间序列的稀疏高斯图模型。我们假设观测由潜在且未观测的隐藏离散自回归过程表征，以此解释数据中的时间相关性。我们采用多元高斯发射分布，并通过图马蹄形先验对状态特定精度矩阵建模以捕捉空间依赖性。我们通过累积收缩先验描述隐藏过程的混合概率，该先验为非活跃成分提供零膨胀参数，还纳入诱导稀疏性的狄利克雷先验，从数据中估计有效状态数。对于后验推断，我们开发采样程序，可估计离散自回归滞后数和状态数，并巧妙避免处理参数空间的维度变化。我们通过多项模拟研究深入考察所提方法的性能，还基于执行潜在学习任务的受试者的功能磁共振成像（fMRI）数据，进一步说明该方法在动态脑连接估计中的应用。
英文摘要：
We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved hidden discrete autoregressive process. We assume multivariate Gaussian emission distributions and capture spatial dependencies by modeling the state-specific precision matrices via graphical horseshoe priors. We characterize the mixing probabilities of the hidden process via a cumulative shrinkage prior that accommodates zero-inflated parameters for non-active components, and further incorporate a sparsity-inducing Dirichlet prior to estimate the effective number of states from the data. For posterior inference, we develop a sampling procedure that allows estimation of the number of discrete autoregressive lags and the number of states, and that cleverly avoids having to deal with the changing dimensions of the parameter space. We thoroughly investigate performance of our proposed methodology through several simulation studies. We further illustrate the use of our approach for the estimation of dynamic brain connectivity based on fMRI data collected on a subject performing a task-based experiment on latent learning
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