Applications of Bayesian latent network models to causal inference and transaction set mining

Although networks are widely used in statistical models as a convenient representation of the relationships between elements of a system, incorporating them within an inferential procedure poses challenges. This dissertation consists of three projects that are unified in their use of a network to represent relationships among the variables being studied and incorporation of the network into a Bayesian framework for inference. Chapter 1 addresses causal inference for time varying treatments using observational data. This problem is discussed from frequentist and Bayesian perspectives, using potential outcomes and graphical model frameworks. We focus on the Bayesian perspective and develop a method for causal inference within this paradigm that accounts for uncertainty in the causal structure of the measured variables. This structure is encoded by a directed acyclic graph (DAG). Our proposed method involves an MCMC sampling procedure in which this DAG is sampled, allowing model averaging over causal structures. Properties of the method are illustrated with simulated data as well as an analysis of data from the Women’s Interagency HIV Study (WIHS), the largest ongoing prospective cohort study of HIV among women in the U.S. Chapter 2 considers the problem of statistical inference for multivariate binary transaction data. We develop a hierarchical model and an MCMC algorithm that features a latent graph to represent associations between products. Properties of this method are illustrated with simulated data as well as data from Instacart, a U.S. company that operates a grocery delivery and pick-up service. Chapter 3 examines longitudinal data from Electronic Health Records (EHR) associated with a pediatric asthma study. This project, a collaboration with the BU School of Public Health and Boston Medical Center, focuses on gaining insight into pediatric lung function, as measured by forced expiratory volume (FEV1%). A longitudinal Hidden Markov Model is developed in which the parameters of the Markov process may be inferred from high dimensional and correlated covariates