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 a latent trajectory. 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 computationally efficient 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 reconstructs epidemic trajectories and estimates key epidemiological parameters, providing an efficient framework for sequential Bayesian inference from imperfect surveillance data.

翻译：从部分观测且含噪声的数据中估计潜在流行病状态和模型参数，仍是传染病建模中的重大挑战。状态空间模型为这类推断提供了连贯的概率框架，然而完全贝叶斯估计常因计算开销过大而受限——评估观测数据似然需对潜在轨迹进行积分。序贯蒙特卡洛平方（SMC$^2$）算法通过将参数外层的SMC采样器与内层粒子滤波器（用于估计截止当前时刻的似然）相结合，为状态与参数的联合推断提供了规范方法。尽管该算法具有理论优势，其嵌套粒子滤波器结构仍带来高昂计算成本，限制了在近实时疫情响应中的常规应用。我们提出集成SMC$^2$（eSMC$^2$）方法，该计算高效变体用集成卡尔曼滤波器（EnKF）替代内层粒子滤波器，以近似每个观测时刻的增量似然。虽然这种替换通过高斯近似引入了偏差，但通过无偏高斯密度估计器消减有限样本效应，并采用状态依赖的观测方差对EnKF进行流行病数据适配，使该方法尤其适用于传染病监测中常见的过度离散发病率数据。基于已知真实值的仿真实验及2022年美国猴痘发病率数据的应用表明，eSMC$^2$在保持与SMC$^2$相当的后验估计质量的同时，实现了显著的计算效率提升。该方法能精确重构流行病轨迹并估计关键流行病学参数，为基于不完善监测数据的序贯贝叶斯推断提供了高效框架。