Center for Automated Learning and Discovery
School of Computer Science, Carnegie Mellon University


Dynamic Nonparametric Bayesian Models
and the Birth-Death Process

Eric P. Xing

December 2005


Keywords: Dirichlet Process, nonparametric Bayesian models, birth-death process, Kalman filter, state-space models, longitudinal data analysis

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.

14 pages

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