Bayesian blind estimation of H-ARMA processes

We present a Bayesian method for the blind estimation of parameters in nonlinear/nonGaussian models. The studied models are called H-ARMA processes. They are generated by a memoryless polynomial transformation of an ARMA process. The nonlinearities are choosen as Hermite polynomials. After recalling the structure of those models and their main properties that have been reported in previous publications, we tackle the problem of parameter estimation only with the knowledge of the output observations. A Bayesian scheme based on data augmentation and MCMC (Monte Carlo Markov chain) samplers is performed. We show that the key point of the algorithm is the sampling of the Markov state process and that the proposed Bayesian method provides well behaved estimators, even when the models are completely non-invertibles