Statistical Methods for Networked Agent Systems: Inference, Design, and Monitoring

Abstract

Many scientific and operational systems are complex dynamic systems of interacting agents. Because behavior unfolds through networks over time, these systems are often only partially observed, may exhibit interference under intervention, and, at large scale, can generate highly complex transition patterns. These features make meaningful statistical analysis difficult. This dissertation develops methods aimed at overcoming these challenges in networked agent systems, leading to three related contributions in inference, design, and monitoring.The first substantive chapter develops a likelihood-based framework for inference on continuous-time epidemic processes observed only through temporally coarsened network and health measurements. By treating discrete observations as coarsened realizations of an underlying continuous-time epidemic--network process, the chapter preserves process-level parameter interpretation across observation regimes. A data-augmented Gibbs sampler is developed to recover the entire continuous-time evolution history with uncertainty by imputing latent recovery times and latent interaction events, enabling posterior inference under partial observation. Simulation studies show that the proposed method closely recovers continuous-time benchmark inference under dense observation and remains stable under more substantial coarsening. An application to the iEpi Bluetooth contact sub-study of the eX-FLU trial yields results similar to those obtained from continuous-time contact data.The second substantive chapter studies causal design for epidemic experiments under network interference. In network settings, treatment assigned to one unit may affect the outcomes of others, and the infection-relevant exposure is induced by a global, path-dependent transmission mechanism that is difficult to encode exactly at the design stage. Motivated by this challenge, the chapter develops a social-contact-network-informed restricted randomization scheme that balances treatment across strata defined by community structure and cross-cluster connectivity. Simulation results show that this design can substantially reduce the RMSE of direct-effect estimation, primarily through variance reduction, when community structure is strong, with gains naturally diminishing as cross-cluster mixing increases.The third substantive chapter studies agent-level anomalous trajectory detection in large-scale agent-flow systems on dynamic networks. Rather than specifying a trajectory-generating mechanism, the chapter develops a scalable Bayesian monitoring framework based on Dynamic Binary Cascade Models (DBCM) for transition behavior and a sequential Bayes-factor detector for persistent regime shifts. On a large synthetic mobility benchmark, the proposed method can achieve strong detection accuracy under effective false positive control and demonstrates the value of explicit counterfactual-style comparison between observed behavior and a stable baseline model.Taken together, these chapters show how structured statistical modeling can support inference, causal design, and monitoring in dependent systems of interacting agents. Across different applications, the dissertation highlights a common lesson: in networked systems, scientifically meaningful conclusions often depend not only on what is observed, but also on how one models the interaction process, the intervention mechanism, or the relevant comparison baseline.