论文标题
贝叶斯推断异质流行模型：在COVID-19的应用中，对长期护理设施的扩散会计
Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities
论文作者
论文摘要
我们提出了一个高维贝叶斯推理框架，用于学习COVID-19模型的异质动力学，并针对Covid-19内外长期护理（LTC）设施的动力学和严重性具有特定的应用。我们开发了一个异质隔室模型，该模型解释了COVID-19的时间变化的差异和在LTC内部和外部LTC设施的严重性的异质性，该设施的特征是分离后的$ \ sim $ 1500尺寸，其特征是时间依赖于时间依赖时间的随机过程。为了推断这些参数，我们使用有关确认，住院和已故病例的数量的报告数据，并在确定性反转方法中进行了适当的后处理，并以适当的正则化为第一步，然后是贝叶斯反转，并具有适当的先验分布。为了解决维数的诅咒和高维推理问题的不良性，我们建议使用独立于维数的Stein变异梯度下降方法，并证明了反问题的内在低维度。我们介绍了新泽西州和德克萨斯州的量化不确定性的推理结果，这些阶段和模式都不同。此外，我们还基于我们对COVID-19的未来轨迹的经验后样本提出了预测和验证结果。
We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in $\sim$1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.
