  The Dirichlet process and its extension, the Pitman-Yor process, are
stochastic processes that take probability distributions as a parameter. These
processes can be stacked up to form a hierarchical nonparametric Bayesian
model. In this article, we present efficient methods for the use of these
processes in this hierarchical context, and apply them to latent variable
models for text analytics. In particular, we propose a general framework for
designing these Bayesian models, which are called topic models in the computer
science community. We then propose a specific nonparametric Bayesian topic
model for modelling text from social media. We focus on tweets (posts on
Twitter) in this article due to their ease of access. We find that our
nonparametric model performs better than existing parametric models in both
goodness of fit and real world applications.
