Banks, David LMa, LiLeBlanc, Patrick M2023-06-082023-06-082023https://hdl.handle.net/10161/27704<p>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.</p>StatisticsBiostatisticsAppliedBayesianBNMAMicrobiomeRecommender SystemsStatisticsDissertation