Generalized Pólya Urn for Time-Varying Pitman-Yor Processes

This article introduces a class of first-order stationary time-varying Pitman-Yor processes. Subsuming our construction of time-varying Dirichlet processes presented in (Caron et al., 2007), these models can be used for time-dynamic density estimation and clustering. Our intuitive and simple construction relies on a generalized Pólya urn scheme. Significantly, this construction yields marginal distributions at each time point that can be explicitly characterized and easily controlled. Inference is performed using Markov chain Monte Carlo and sequential Monte Carlo methods. We demonstrate our models and algorithms on epidemiological and video tracking data.