UC Irvine

Modern datasets often feature complex structures and large numbers of observations, raising both challenges and opportunities for statistical analysis. In this dissertation, we develop novel Bayesian methods to analyze networks and multivariate time-series data. For network data we propose a random graph model that uncovers community structure by thinning edges from sparse networks generated via infinite point-process priors. Our approach allows entities to belong to multiple communities and learns the number of latent communities active in the network. We develop a Monte Carlo inference algorithm featuring sub-quadratic complexity in the number of nodes, unlike most dense block models. We show improved performance over existing models on real-world social and biological networks and explore finite approximations of infinite priors as a promising step toward scaling our methods to networks with hundreds of thousands of nodes. We then address the analysis of multivariate time series from multiple subjects, aiming to identify both subject clusters with similar temporal behavior and time-varying clusters of correlated measurements. We propose a Bayesian temporal biclustering model featuring nested partitions: a static partition of subjects induces dynamic measurement clusters. Applications to fMRI and EEG data illustrate the model’s utility, and simulations show strong recovery of true clusters, both in settings with high and minimal between-subject or time dependence.