Estimating latent epidemic states and model parameters from partially observed, noisy data remains a major challenge in infectious disease modeling. State-space formulations provide a coherent probabilistic framework for such inference, yet fully Bayesian estimation is often computationally prohibitive because evaluating the observed-data likelihood requires integration over all latent trajectories. The Sequential Monte Carlo squared (SMC$^2$) algorithm offers a principled approach for joint state and parameter inference, combining an outer SMC sampler over parameters with an inner particle filter that estimates the likelihood up to the current time point. Despite its theoretical appeal, this nested particle filter imposes substantial computational cost, limiting routine use in near-real-time outbreak response. We propose Ensemble SMC$^2$ (eSMC$^2$), a scalable variant that replaces the inner particle filter with an Ensemble Kalman Filter (EnKF) to approximate the incremental likelihood at each observation time. While this substitution introduces bias via a Gaussian approximation, we mitigate finite-sample effects using an unbiased Gaussian density estimator and adapt the EnKF for epidemic data through state-dependent observation variance. This makes our approach particularly suitable for overdispersed incidence data commonly encountered in infectious disease surveillance. Simulation experiments with known ground truth and an application to 2022 United States (U.S.) monkeypox incidence data demonstrate that eSMC$^2$ achieves substantial computational gains while producing posterior estimates comparable to SMC$^2$. The method accurately recovers latent epidemic trajectories and key epidemiological parameters, providing an efficient framework for sequential Bayesian inference from imperfect surveillance data.

翻译：从部分观测的噪声数据中估计潜藏的流行病状态与模型参数，始终是传染病建模领域的核心挑战。状态空间模型为此类推断提供了协调的概率框架，但完全贝叶斯估计常因计算量过大而难以实现——评估观测数据似然需对所有潜在轨迹进行积分。序贯蒙特卡洛平方（SMC$^2$）算法为联合状态与参数推断提供了理论严谨的方法，其外层SMC采样器遍历参数空间，内层粒子滤波器则估计截至当前时刻的似然。尽管理论优势显著，这种嵌套粒子滤波器计算代价高昂，限制了其在近实时疫情响应中的常规应用。本文提出集合SMC$^2$（eSMC$^2$），一种可扩展的改进方案：用集合卡尔曼滤波器（EnKF）替代内层粒子滤波器，以近似每个观测时刻的增量似然。虽然该替代通过高斯近似引入偏差，但我们采用无偏高斯密度估计器缓解有限样本效应，并通过状态依赖的观测方差调整EnKF以适应流行病数据特性。这使得该方法特别适用于传染病监测中常见的过离散发病数据。基于已知真实参数的仿真实验及对2022年美国猴痘发病数据的实证应用表明，eSMC$^2$在获得与SMC$^2$可比的后验估计的同时，实现了显著的计算效率提升。该方法能准确还原潜藏流行轨迹与关键流行病学参数，为基于非完善监测数据的序贯贝叶斯推断提供了高效框架。