Point Process Models for Heterogeneous Event Time Data

Interaction event times observed on a social network provide valuable information for social scientists to gain insight into complex social dynamics that are challenging to understand. However, it can be difficult to accurately represent the heterogeneity in the data and to model the dependence structure in the network system. This requires flexible models that can capture the complicated dynamics and complex patterns. Point process models offer an elegant framework for modeling event time data. This dissertation concentrates on developing point process models and related diagnostic tools, with a real data application involving an animal behavior network. In this dissertation, we first propose a Markov-modulated Hawkes process (MMHP) model to capture the sporadic and bursty patterns often observed in event time data. A Bayesian inference procedure is developed to evaluate the likelihood by using a variational approximation and the forward-backward algorithm. The validity of the proposed model and associated estimation algorithms is demonstrated using synthetic data and the animal behavior data. Facilitated by the power of the MMHP model, we construct network point process models th