Geometric Stick-Breaking Processes for Continuous-Time Nonparametric Modeling

Abstract

This paper is concerned with the construction of a continuous parameter sequence of random probability measures and its application for modeling random phenomena evolving in continuous time. At each time point we have a random probability measure which is generated by a Bayesian nonparametric hierarchical model, and the dependence structure is induced through a Wright-Fisher diffusion with mutation. The sequence is shown to be a stationary and reversible diffusion taking values on the space of probability measures. A simple estimation procedure for discretely observed data is presented and illustrated with simulated and real data sets.Bayesian non-parametric inference, continuous time dependent random measure, Markov process, measure-valued process, stationary process, stick-breaking process