贝叶斯广义网络自回归模型：结构化收缩与持久性先验
Bayesian Generalized Network Autoregressive Model with Structured Shrinkage and Persistence Priors
- Human-Centered Artificial Intelligence Research Institute, Ewha Womans University（梨花女子大学人类中心人工智能研究所）
- Department of Statistics and Actuarial Science, Soongsil University（崇实大学统计与精算科学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出贝叶斯广义网络自回归模型，结合结构化收缩与持久性先验，无需BIC选择即可保持预测精度，并提供参数与预测不确定性推断。
AI中文摘要：
我们提出了一种贝叶斯广义网络自回归（BGNAR）模型，用于处理其分量序列与已知网络节点相关联的多元时间序列。所提出的框架将广义网络自回归（GNAR）模型的简约网络结构与从贝叶斯向量自回归（BVAR）建模中改编的结构化收缩和持久性先验相结合。我们将明尼苏达型收缩应用于自有滞后和网络滞后系数，先验方差随时间滞后以及网络效应的邻域阶数递减。自有滞后系数上的分层先验允许信息在节点间共享，同时保留节点特异性异质性。我们进一步将系数和与虚拟初始观测先验适配到GNAR参数化中。后验推断通过吉布斯采样器进行。模拟研究表明，BGNAR可以在不同数据集上使用相同的刻意过度指定的时间和邻域结构，而无需数据集特定的BIC阶数选择，同时保持与BIC选择的GNAR相当的预测准确性，并在所考虑的设置中优于无限制的BVAR基准。结构化先验将弱支持的系数正则化至该固定模型内的零。动态系数的后验分布和未来观测的后验预测分布提供了参数和预测不确定性的直接量化。对风速网络的应用表明，BGNAR实现了与GNAR相当的点预测性能，同时额外提供了对自有滞后和网络滞后效应的后验推断以及后验预测不确定性。
英文摘要：
We propose a Bayesian generalized network autoregressive (BGNAR) model for multivariate time series whose component series are associated with the nodes of a known network. The proposed framework combines the parsimonious network structure of the generalized network autoregressive (GNAR) model with structured shrinkage and persistence priors adapted from Bayesian vector autoregressive (BVAR) modeling. We adapt Minnesota-type shrinkage to both own-lag and network-lag coefficients, with prior variances decreasing over temporal lags and, for network effects, neighborhood orders. A hierarchical prior on the own-lag coefficients allows information to be shared across nodes while retaining node-specific heterogeneity. We further adapt the sum-of-coefficients and dummy-initial-observation priors to the GNAR parameterization. Posterior inference is performed using a Gibbs sampler. Simulation studies show that BGNAR can use the same deliberately over-specified temporal and neighborhood structure across datasets without dataset-specific BIC order selection, while maintaining forecasting accuracy comparable to BIC-selected GNAR and outperforming the unrestricted BVAR benchmark in the settings considered. The structured prior regularizes weakly supported coefficients toward zero within this fixed model. Posterior distributions for the dynamic coefficients and posterior predictive distributions for future observations provide direct quantification of parameter and predictive uncertainty. An application to a wind-speed network demonstrates that BGNAR achieves point-forecast performance comparable to GNAR while additionally providing posterior inference on own-lag and network-lag effects and posterior predictive uncertainty.
