Bayesian Inference for Linear Dynamic Models with Dirichlet Process Mixtures

Details Bayesian Inference for Linear Dynamic Models with Dirichlet Process Mixtures Bayesian Inference for Linear Dynamic Models with Dirichlet Process Mixtures

2007-02-08

arxiv.org/abs/math/0702225v1

IEEE Transactions on Signal Processing (2006)

Mathematics

Statistics Theory

Scientific paper

10.1109/TSP.2007.900167

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.

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