  In this dissertation, we develop nonparametric Bayesian models for biomedical
data analysis. In particular, we focus on inference for tumor heterogeneity and
inference for missing data. First, we present a Bayesian feature allocation
model for tumor subclone reconstruction using mutation pairs. The key
innovation lies in the use of short reads mapped to pairs of proximal single
nucleotide variants (SNVs). In contrast, most existing methods use only
marginal reads for unpaired SNVs. In the same context of using mutation pairs,
in order to recover the phylogenetic relationship of subclones, we then develop
a Bayesian treed feature allocation model. In contrast to commonly used feature
allocation models, we allow the latent features to be dependent, using a tree
structure to introduce dependence. Finally, we propose a nonparametric Bayesian
approach to monotone missing data in longitudinal studies with non-ignorable
missingness. In contrast to most existing methods, our method allows for
incorporating information from auxiliary covariates and is able to capture
complex structures among the response, missingness and auxiliary covariates.
Our models are validated through simulation studies and are applied to
real-world biomedical datasets.
