Dynamic density estimation with diffusive Dirichlet mixtures

TL;DR

This paper presents a novel nonparametric prior for dynamic density estimation using diffusive Dirichlet mixtures, enabling flexible modeling of time-varying distributions with continuous paths.

Contribution

It introduces a new class of time-dependent Dirichlet process mixtures using Wright-Fisher diffusions, enhancing flexibility and tractability in dynamic density modeling.

Findings

Effective modeling of evolving densities demonstrated on simulated data.

Flexible extension to multi-parameter GEM processes shown.

Method provides a tractable approach for Bayesian inference in dynamic settings.

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.