Inference for Mechanistic Network Models and Visualization of Real-World Network Data

Abstract

Network analysis enables a comprehensive investigation of disease transmission dynamics by modeling and analyzing interactions among individuals and their connections. Mechanistic network models allow for modeling and modifying individual-level real-world behaviours that are crucial to most intervention strategies involving disease transmission, especially in sexually transmitted diseases such as HIV/AIDS. However, this class of models requires special analytical considerations due to the intractability of the likelihood function. Furthermore, optimizing the visualization of real-world network structures is crucial for both exploratory data analysis and for developing specific hypotheses. Current visualization methods, when reducing the dimensionality of networks to 2D layouts, are very sensitive to the structure of the observed network. They also do not consider nodal covariates when computing node locations, which is unfortunate because the covariates might often carry information about network structure that could be leveraged in network visualization. This dissertation introduces new methods to analyze mechanistic network models using an approximate Bayesian scheme and new methods to visualize network data accounting for nodal covariates to compensate for imperfect structural information. The methods presented provide scalable approaches for analyzing, visualizing, and, hence, making use of real-world network models and network data. Chapter 1 presents a novel method to sample a network at two time points to improve inference. Often, network data are, or can be, collected longitudinally in waves. By constructing summary statistics that include information from two longitudinal samples of an evolving network, we show that accuracy of parameter inference in a mechanistic model can drastically improve as a function of the time between the two samples. This allows us to better guide study designs involving network data such as those in HIV/AIDS cohort studies. We validate this method on a previously published mechanistic network model governing the sexual connections among men who have sex with men. Chapter 2 explores the benefits of directly including nominal nodal information in the standard Fruchterman-Reingold network visualization algorithm. An application of this method helps uncover an additional layer of insights into societal relationships in a village in rural India. Chapter 3 introduces a principled, model-based approach to incorporate nodal information in network visualization. This method adds a layer of robustness to real-world network data visuals as we demonstrate using both simulations and data from the National Longitudinal Study of Adolescent to Adult Health (Add Health).