Dynamic density estimation with diffusive Dirichlet mixtures

Abstract

We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose sections are continuous or discrete distributions depending on the choice of kernel. The construction exploits the widely used stick-breaking representation of the Dirichlet process and induces the time dependence by replacing the stick-breaking components with one-dimensional Wright-Fisher diffusions. These features combine appealing properties of the model, inherited from the Wright-Fisher diffusions and the Dirichlet mixture structure, with great flexibility and tractability for posterior computation. The construction can be easily extended to multi-parameter GEM marginal states, which include, for example, the Pitman--Yor process. A full inferential strategy is detailed and illustrated on simulated and real data.

Published at http://dx.doi.org/10.3150/14-BEJ681 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Bayesian Inference for Linear Dynamic Models with Dirichlet Process Mixtures
• Generalized Polya Urn for Time-varying Dirichlet Process Mixtures
• Alpha-diversity processes and normalized inverse-Gaussian diffusions

Cited by in corpus (5)

• Exact simulation of the Wright-Fisher diffusion
• Bayesian nonparametric forecasting of monotonic functional time series
• Conjugacy properties of time-evolving Dirichlet and gamma random measures
• Clustering dynamics in a class of normalised generalised gamma dependent priors
• The Rescaled Polya Urn and the Wright-Fisher process with mutation