Dynamic Nonparametric Bayesian Models And the Birth-Death Process

When modeling longitudinal data using a set of hidden processes such as state-space models, a common assumption is that the number of hidden processes is fixed, and all hidden processes have the same life span (i.e., all start at the onset of the data stream and terminate at the end of the data stream). In this report I outline a framework of modeling complex longitudinal data using a birth-death process, in which hidden processes and emerge, evolve, and extinct over time. The model is built on top of a temporally evolving Dirichlet process, and thus allow the total number of hidden processes to be unbounded. I also derive a Gibbs sampling algorithm for inference on this model.