AI 中文总结
研究部分观测下流行病传播模型的可识别性与推断，建立统一框架，推导信息矩阵，量化信息损失，研究观测因素对参数估计的影响，为评估监测策略提供依据，模拟验证框架准确性，奠定统计推断理论基础。
AI 中文摘要
动态网络上流行病传播的推断受到潜伏感染时间、不完整接触历史、不完美观测和外部感染源的根本限制。尽管对于部分观测的流行病过程有连贯的似然公式，但对于这种观测机制下统计推断的理论极限知之甚少。本文为研究动态接触网络上观测到的流行病传播模型中的可识别性和费希尔信息建立了一个统一框架。我们建立了结构和局部可识别性的条件，推导了观测和完整数据信息矩阵，并通过缺失信息分解量化了未观测到的传播事件和缺失网络信息导致的信息损失。我们进一步研究了观测频率、网络覆盖范围和测量精度如何影响参数可估计性和统计效率，为评估监测策略提供了原则基础。模拟研究表明，所提出的框架准确地刻画了观测设计、统计信息和参数估计之间的关系，理论预测与有限样本性能紧密匹配。所提出的框架阐明了观测设计、可识别性和推断精度之间的关系，并为部分观测的流行病传播模型中的统计推断提供了理论基础。
英文摘要
Inference for epidemic transmission on dynamic networks is fundamentally limited by latent infection times, incomplete contact histories, imperfect observation, and external sources of infection. Although coherent likelihood formulations are available for partially observed epidemic processes, considerably less is known about the theoretical limits of statistical inference under such observation mechanisms. This paper develops a unified framework for studying identifiability and Fisher information in epidemic transmission models observed on dynamic contact networks. We establish conditions for structural and local identifiability, derive observed and complete-data information matrices, and quantify information loss arising from unobserved transmission events and missing network information through a missing-information decomposition. We further investigate how observation frequency, network coverage, and measurement accuracy influence parameter estimability and statistical efficiency, providing a principled basis for evaluating surveillance strategies. Simulation studies demonstrate that the proposed framework accurately characterises the relationship between observation design, statistical information, and parameter estimation, with theoretical predictions closely matching finite-sample performance. The proposed framework clarifies the relationship between observation design, identifiability, and inferential precision, and provides a theoretical foundation for statistical inference in partially observed epidemic transmission models.
Comments23 pages, 7 figures
