Stochastic Process Models on Dynamic Networks

Abstract

<p>We present novel model frameworks and inference procedures for stochastic point processes on dynamic networks. The point process can be defined for a random phenomenon that spreads among the network nodes, and for the temporally evolving network itself. Methods development is motivated by the needs of health and social science data, where partial observations or latent structures are common and create challenges to likelihood-based inference. In this dissertation, we will discuss parameter estimation techniques that can handle these latent variables and make effective use of the complete data likelihood for efficient inference. We start with developing individualized continuous time Markov chain models for stochastic epidemics on a dynamic contact network. Data-augmentation algorithms are designed to address partial observations (such as missing infection and recovery times) in epidemic data while accommodating the network dynamics. We apply the frameworks to the study of non-pharmaceutical interventions in a college population. Next, we move on to study the higher-order latent structures of dynamic inter-personal interactions by combining a multi-resolution spatio-temporal stochastic process with a latent factor model for a dynamic social network. We apply it to analyzing basketball data where the discovered latent structure defines a metric that helps evaluate the quality of game play. Finally, we discuss extensions to a non-Markovian setting of self and mutually exciting point processes (Hawkes processes). We utilize the branching structure of the Hawkes processes to uncover the latent replying structure of a group conversation, which can be further employed to quantitatively measure individual social impact. </p>