Nonlinear regression using smooth Bayesian estimation

Abstract : This paper proposes a new Bayesian strategy for the estimation of smooth parameters from nonlinear models. The observed signal is assumed to be corrupted by an independent and non identically (colored) Gaussian distribution. A prior enforcing a smooth temporal evolution of the model parameters is considered. The joint posterior distribution of the unknown parameter vector is then derived. A Gibbs sampler coupled with a Hamiltonian Monte Carlo algorithm is proposed which allows samples distributed according to the posterior of interest to be generated and to estimate the unknown model parameters/hyperparameters. Simulations conducted with synthetic and real satellite altimetric data show the potential of the proposed Bayesian model and the corresponding estimation algorithm for nonlinear regression with smooth estimated parameters.
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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2015), Apr 2015, South Brisbane, QLD, Australia. Proceedings of ICASSP 2015, pp. 2634-2638, 2015
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Abderrahim Halimi, Corinne Mailhes, Jean-Yves Tourneret. Nonlinear regression using smooth Bayesian estimation. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2015), Apr 2015, South Brisbane, QLD, Australia. Proceedings of ICASSP 2015, pp. 2634-2638, 2015. 〈hal-01485021〉

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