用于贝叶斯趋势滤波的图依赖收缩先验
Graph-dependent shrinkage priors for Bayesian trend filtering
AI总结：
该研究提出图依赖收缩先验的贝叶斯趋势滤波框架，通过在趋势、局部收缩、MCMC采样环节利用图，提升了数据估计精度与计算效率，成功应用于美国县域失业数据的时空建模与预测。
AI中文摘要：
许多常见的数据依赖关系可由图表征：时间序列数据是序列型（链状图），图像是像素型（格状图），区域数据由相邻单元定义（空间邻接图）等。图趋势滤波旨在对这类数据进行平滑和预测，但传统趋势滤波仅将图用于趋势估计，这限制了其适应性，在存在缺失数据时表现脆弱，且缺乏不确定性量化，还面临一定计算挑战。我们针对（图）依赖数据提出了一套全面的贝叶斯框架以解决这些局限，该方法在三个关键环节利用图：1）趋势环节，以实现平滑、插补和预测；2）局部收缩环节，以提升适应性和精度；3）MCMC采样算法环节，通过稀疏和带状运算实现可扩展的后验（预测）推断。针对所提出的图依赖收缩先验，我们研究了其局部集中性和适应性性质，并建立了后验正则性的条件。模拟研究表明，相较于当前最先进的频率学派和贝叶斯学派替代方法，该框架能提供更准确的点估计、更精确的区间估计，且计算效率极具竞争力。我们将该方法应用于2020年新冠疫情失业冲击期间美国本土各州所有县的时空建模与失业数据预测。
英文摘要：
Many common data dependencies can be characterized by graphs: time series data are sequential (chain graph), images appear as pixels (lattice graph), areal data are defined by neighboring units (spatial adjacency graph), etc. Graph trend filtering seeks to smooth and predict such data. However, classical trend filtering only incorporates the graph for estimation of the trend, which limits its adaptivity, and is brittle in the presence of missing data. Further, it lacks uncertainty quantification and faces certain computing challenges. We address these limitations with a comprehensive Bayesian framework for (graph-) dependent data. Our approach leverages the graph at three critical junctures: 1) the trend, to enable smoothing, imputation, and prediction; 2) the local shrinkage, to enhance adaptivity and precision; and 3) the MCMC sampling algorithm, to deliver scalable posterior (predictive) inference via sparse and banded operations. For the proposed graph-dependent shrinkage priors, we study the local concentration and adaptivity properties and establish conditions for posterior propriety. Simulation studies demonstrate that, relative to state-of-the-art frequentist and Bayesian alternatives, this framework provides more accurate point estimates, more precise interval estimates, and highly competitive computing. We apply our methods for spatio-temporal modeling and forecasting of local area unemployment data for every county in the continental U.S. during the 2020 COVID-19 unemployment shock.
