This thesis makes contributions to the area of nonparametric Bayesian methods and applications in two distinct subject areas. One is about classification problems in machine learning. The other is on network meta-analysis in the field of clinical trials. We start by introducing some basic facts about Dirichlet distributions and Dirichlet processes. Nonparametric Bayesian methods and models and their construction follows. We then provide a survey of the existing Markov chain Monte Carlo inference algorithms for Dirichlet Process Mixture models (DPMM), which is followed by a detailed description of these methods to the application problems.

In the first application, we introduce the idea of incorporating wavelet transform and dimension reduction techniques with the probabilistic mixtures to perform complex classification tasks. These tasks involve distinguishing stages of retinal detachment process for confocal microscopic cross-sectional retinal layer images. In general, the progression of retinal detachment process is associated with different degrees of deformation of retinal layers and redistribution of molecules. Yet this leads to many challenges including lack of data in subcategories, inconsistent experimental conditions, huge intra-class variations, and different angles of target objects. We validate the excellent out-of-sample prediction performance of the model by repeated 10-fold cross-validation.

In the second application, we develop novel DPMM-based hierarchical framework to model the uncertainty and heterogeneity of the historical trials into the non-inferiority (NI) trials. In NI trials, we compare the test treatment with an efficacious active control treatment when a direct comparison between test treatment and placebo is not available. Our goal is to demonstrate that the test treatment is not inferior to the active control by a pre-specified margin instead of directly showing the superiority of the test treatment over placebo. In the real clinical data examples, the model provides a more reliable estimate of the control given its effect in other trials in the network. It can further answer other questions of interest, such as comparative effectiveness of the test treatment among its comparators. More importantly, the model provides an opportunity for disproportionate randomization or the use of small sample sizes by allowing borrowing of information from a network of historical trials to draw explicit conclusions on non-inferiority.