Geometric stick-breaking processes for continuous-time Bayesian nonparametric modeling

We propose a new class of time dependent random probability measures and show how this can be used for Bayesian nonparametric inference in continuous time. By means of a nonparametric hierarchical model we define a random process with geometric stick-breaking representation and dependence structure induced via a one dimensional diffusion process of Wright–Fisher type. The sequence is shown to be a strongly stationary measure-valued process with continuous sample paths which, despite the simplicity of the weights structure, can be used for inferential purposes on the trajectory of a discretely observed continuous-time phenomenon. A simple estimation procedure is presented and illustrated with simulated and real financial data.