Bayesian Inference for Linear Dynamic Models with Dirichlet Process Mixtures

François Caron; Manuel Davy; Arnaud Doucet; Emmanuel Duflos; Philippe Vanheeghe

Bayesian Inference for Linear Dynamic Models with Dirichlet Process Mixtures

François Caron ¹ Manuel Davy ^{1, 2} Arnaud Doucet ³ Emmanuel Duflos ^{1, 2} Philippe Vanheeghe ^{1, 2}

LIFL - Laboratoire d'Informatique Fondamentale de Lille, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal, Inria Lille - Nord Europe

2 LAGIS-SI

LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal

3 Statistics - Department of Statistics

Abstract : Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures is introduced. Efficient Markov chain Monte Carlo and Sequential Monte Carlo methods are then developed to perform optimal batch and sequential estimation in such contexts. The algorithms are applied to blind deconvolution and change point detection. Experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts.

Keywords : Bayesian nonparametrics Dirichlet process mixture (DPM) Markov chain Monte Carlo (MCMC) particle filter Rao-Blackwellization

Document type :

Journal articles

Domain :

Mathematics [math] / Statistics [math.ST]

Statistics [stat] / Statistics Theory [stat.TH]

Complete list of metadatas

https://hal.inria.fr/inria-00129646
Contributor : Manuel Davy <>
Submitted on : Thursday, February 8, 2007 - 5:16:51 PM
Last modification on : Thursday, February 21, 2019 - 10:52:49 AM
Long-term archiving on : Tuesday, April 6, 2010 - 11:40:19 PM

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