部分观测动态网络上流行病过程的完整数据似然性
A Complete-Data Likelihood for Epidemic Processes on Partially Observed Dynamic Networks
AI总结：
研究部分观测动态网络上传染病传播推断难题，提出统一完整数据似然性框架，耦合SEIR过程与动态网络及观测模型，推导完整数据似然性，为推断提供基础，揭示模型关系并助力复杂传播过程分析。
AI中文摘要：
在动态接触网络上对传染病传播进行推断时，由于潜在感染时间、部分观测的网络演化、接触数据中的测量误差以及来自观测人群之外的感染等因素而变得复杂。现有基于似然性的方法通常分别应对这些挑战，且常依赖如完全观测网络、封闭人群或用症状发作替代感染时间等限制性假设。我们为在部分观测动态网络上演变的流行病过程开发了一个统一的完整数据似然性框架。该框架将疾病进展、网络演化和观测机制表示为一个共同概率框架内相互作用的连续时间随机过程。具体而言，将易感-暴露-感染-康复（SEIR）流行病过程与状态依赖的动态接触网络及症状和接触的显式观测模型相结合。所得框架考虑了潜在潜伏期、间歇性网络观测、接触测量误差和外部感染压力，同时保留了连贯的似然性结构。我们的主要贡献是推导了部分观测下联合流行病-网络过程的完整数据事件历史似然性。该似然性为基于数据增强的似然性和贝叶斯推断提供了严格基础，阐明了疾病进展和接触动态的信息如何共同决定参数可估计性，并揭示了现有广泛的流行病网络模型是特殊情况。更一般地，该框架有助于对演变网络上部分观测的相互作用随机系统进行统计推断，并为复杂传播过程的不确定性感知分析奠定基础。
英文摘要：
Inference for infectious disease transmission on dynamic contact networks is complicated by latent infection times, partially observed network evolution, measurement error in contact data, and infection originating from outside the observed population. Existing likelihood-based approaches typically address these challenges separately and often rely on restrictive assumptions such as fully observed networks, closed populations, or symptom onset as a surrogate for infection time. We develop a unified complete-data likelihood framework for epidemic processes evolving on partially observed dynamic networks. The proposed formulation represents disease progression, network evolution, and observation mechanisms as interacting continuous-time stochastic processes within a common probabilistic framework. Specifically, we couple a susceptible-exposed-infectious-removed (SEIR) epidemic process with a status-dependent dynamic contact network and explicit observation models for symptoms and contacts. The resulting framework accommodates latent incubation periods, intermittent network observation, contact measurement error, and external infection pressure while preserving a coherent likelihood structure. Our principal contribution is the derivation of a complete-data event-history likelihood for the joint epidemic-network process under partial observation. The likelihood provides a rigorous foundation for likelihood-based and Bayesian inference through data augmentation, clarifies how information from disease progression and contact dynamics jointly determines parameter estimability, and reveals a broad class of existing epidemic network models as special cases. More generally, the framework contributes to statistical inference for partially observed interacting stochastic systems on evolving networks and establishes a foundation for uncertainty-aware analysis of complex transmission processes.
