Open Access
May 2016 Dynamic density estimation with diffusive Dirichlet mixtures
Ramsés H. Mena, Matteo Ruggiero
Bernoulli 22(2): 901-926 (May 2016). DOI: 10.3150/14-BEJ681


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.


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Ramsés H. Mena. Matteo Ruggiero. "Dynamic density estimation with diffusive Dirichlet mixtures." Bernoulli 22 (2) 901 - 926, May 2016.


Received: 1 September 2013; Revised: 1 May 2014; Published: May 2016
First available in Project Euclid: 9 November 2015

zbMATH: 06562300
MathSciNet: MR3449803
Digital Object Identifier: 10.3150/14-BEJ681

Keywords: Density estimation , Dirichlet process , Hidden Markov model , Nonparametric regression , Pitman–Yor process , Wright–Fisher diffusion

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 2 • May 2016
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