A semiparametric Bayesian approach to Wiener system identification

We consider a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process (GP) model for the static nonlinearity. The GP model is a exible model that can describe di erent types of nonlinearities while avoiding making strong assumptions such as monotonicity. We derive an inferential method based on recent advances in Monte Carlo statistical methods, known as Particle Markov Chain Monte Carlo (PMCMC). The idea underlying PMCMC is to use a particle lter (PF) to generate a sample state trajectory in a Markov chain Monte Carlo sampler. We use a recently proposed PMCMC sampler, denoted particle Gibbs with backward simulation, which has been shown to be e cient even when we use very few particles in the PF. The resulting method is used in a simulation study to identify two di erent Wiener systems with noninvertible nonlinearities.