Estimation of the nonlinearity degree for polynomial autoregressiv processes with RJMCMC

Despite the popularity of linear process models in signal and image processing, various real life phenomena exhibit nonlinear characteristics. Compromising between the realistic and computationally heavy nonlinear models and the simplicity of linear estimation methods, linear in the parameters nonlinear models such as polynomial autoregressive (PAR) models have been accessible analytical tools for modelling such phenomena. In this work, we aim to demonstrate the potentials of Reversible Jump Markov Chain Monte Carlo (RJMCMC) which is a successful statistical tool in model dimension estimation in nonlinear process identification. We explore the capability of RJMCMC in jumping not only between spaces with different dimensions, but also between different classes of models. In particular, we demonstrate the success of RJMCMC in sampling in linear and nonlinear spaces of varying dimensions for the estimation of PAR processes.