Accurate and reliable forecasting of epidemic incidences is critical for public health preparedness, yet it remains a challenging task due to complex nonlinear temporal dependencies and heterogeneous spatial interactions. Often, point forecasts generated by spatiotemporal models are unreliable in assigning uncertainty to future epidemic events. Probabilistic forecasting of epidemics is therefore crucial for providing the best or worst-case scenarios rather than a simple, often inaccurate, point estimate. We present deep spatiotemporal engression methods to generate accurate and reliable probabilistic forecasts on low-frequency epidemic datasets. The proposed methods act as distributional lenses, and out-of-sample probabilistic forecasts are generated by sampling from the trained models. Our frameworks encapsulate lightweight deep generative architectures, wherein uncertainty is quantified endogenously, driven by a pre-additive noise component during model construction. We establish geometric ergodicity and asymptotic stationarity of the spatiotemporal engression processes under mild assumptions on the network weights and pre-additive noise process. Comprehensive evaluations across six epidemiological datasets over three forecast horizons demonstrate that the proposal consistently outperforms several temporal and spatiotemporal benchmarks in both point and probabilistic forecasting. Additionally, we explore the explainability of the proposal to enhance the models' practical application for informed, timely public health interventions.

翻译：流行病发病率的准确可靠预测对公共卫生应急准备至关重要，但由于复杂的非线性时间依赖性和异质性空间相互作用，这仍是一项具有挑战性的任务。时空模型生成的单点预测在分配未来流行病事件的不确定性方面往往不可靠。因此，流行病的概率预测对于提供最佳或最坏情况而非简单且通常不准确的单点估计至关重要。我们提出了深度时空外推方法，以在低频流行病数据集上生成准确可靠的概率预测。所提方法作为分布透镜，通过从训练模型中采样生成样本外概率预测。我们的框架封装了轻量级深度生成架构，其中不确定性通过模型构建过程中的前置加性噪声分量进行内源性量化。我们在网络权重和前置加性噪声过程的温和假设下，建立了时空外推过程的几何遍历性和渐近平稳性。在三个预测时间跨度上对六个流行病学数据集的综合评估表明，该方案在单点预测和概率预测方面均持续优于多个时间及时空基准模型。此外，我们探索了该方案的可解释性，以增强模型在知情、及时的公共卫生干预中的实际应用。