# Dynamic density estimation with diffusive Dirichlet mixtures

arXiv: https://arxiv.org/abs/1410.2477 · HTML: https://mlsanity.com/paper/1410.2477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2014.

## Built on by (most cited first, 1 of 1)

- [TAKDE: Temporal Adaptive Kernel Density Estimator for Real-Time Dynamic Density Estimation](https://mlsanity.com/paper/2203.08317/) (2022)

## Abstract (arXiv)

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.