Nonlinear regression using smooth Bayesian estimation

Abderrahim Halimi (1, 2) , Corinne Mailhes (1, 2) , Jean-Yves Tourneret (3, 2, 4)

1 IRIT-SC - Signal et Communications
2 TéSA - Télécommunications Spatiales et Aéronautiques - Telecommunications for Space ant Aeronautics
3 IRIT-MINDS - CoMputational imagINg anD viSion
4 Toulouse INP - Institut National Polytechnique (Toulouse)

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.

Mots clés: Parameter estimation; MCMC; Bayesian algorithm; Hamiltonian Monte-Carlo; Radar altimetry

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

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. pp. 2634-2638. ⟨hal-01485021⟩