Bayesian latent space approaches to network analysis

In our interconnected world, networks permeate various aspects of life, from social interactions to biological systems. This research delves into the world of network analysis, a field that helps us understand and interpret the connections in these networks. We introduced new methods that make it easier and more effective to analyze these connections, focusing on two main areas: how we group connections (edge clustering) and how we measure the influence individuals have on each other (social influence estimation). In the realm of edge clustering, a significant challenge is determining the optimal number of clusters. Our research proposed an innovative extension to the current edge clustering approach, enabling automatic determination of cluster numbers and therefore, significantly cutting down the computational effort required for such analyses. The second part of the dissertation focuses on accurately measuring how much people or entities influence each other within a network, while taking into account the natural tendency for similar individuals to associate (homophily). We utilized latent space models to estimate latent homophily and adjusted for this factor in social influence estimation. Our simulation studies provided compelling evidence that homophily-adjusted influence models yield more precise estimates than those that overlook latent homophily.