Topics in Applied Statistics

One of the fundamental goals of statistics is to develop methods which provide improved inference in applied problems. This dissertation will introduce novel methodology and review state-of-the-art existing methods in three different areas of applied statistics. Chapter 2 focuses on modelling subcommunity dynamics in gut microbiome data. Existing methods ignore cross-sample heterogeneity in subcommunity composition; we propose a novel mixed-membership model which models cross-sample heterogeneity using the phylogenetic tree and as a result is robust to mispecifying the number of subcommunities. Chapter 3 reviews state-of-the-art methods in recommender systems, including collaborative filtering, content-based filtering, hybrid recommenders, and active recommender systems. Existing literature has focused primarily on bespoke applications; statisticians have an opportunity to build recommender system theory. Chapter 4 proposes a novel method of accounting for time-based design inconsistencies in Bayesian network meta-analysis models and discovers non-linear time trends in the effectiveness of vancomycin as a MRSA treatment. Chapter 5 provides some concluding remarks.