2019/03/08 by Jing Wu, Wu, Jing, Owen G. Ward +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #Diffusion and Search Dynamics #FOS: Computer and information sciences #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1903.03223
openalex publication_date 2019/03/08 · openalex created_date 2019/03/22 · openalex updated_date 2026/07/28
Modeling event dynamics is central to many disciplines. Patterns in observed event arrival times are commonly modeled using point processes. Such event arrival data often exhibits self-exciting, heterogeneous and sporadic trends, which is challenging for conventional models. It is reasonable to assume that there exists a hidden state process that drives different event dynamics at different states. In this paper, we propose a Markov Modulated Hawkes Process (MMHP) model for learning such a mixture of event dynamics and develop corresponding inference algorithms. Numerical experiments using synthetic data demonstrate that MMHP with the proposed estimation algorithms consistently recover the true hidden state process in simulations, while email data from a large university and data from an animal behavior study show that the procedure captures distinct event dynamics that reveal interesting social structures in the real data.