Bayesian Parameter Estimation and Model Selection of a Nonlinear Dynamical System using Reversible Jump Markov Chain Monte Carlo

The aim of this paper is to demonstrate the potential of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm when applied to system identification problems which involve both parameter estima- tion and model selection. Within the context of Bayesian Inference, Markov Chain Monte Carlo (MCMC) methods have been used for a long period of time to address the parameter estimation of linear and nonlinear systems, which are described approximately by a model. It is often the case that there are a set of competing model structures that could potentially produce good approximations of the real system - this raises the issue of model selection. Even though they address parameter estimation, many MCMC samplers cannot address model selection. As an extension to one of the most well known MCMC samplers, the Metropolis-Hastings algorithm, the RJMCMC algorithm is a MCMC method that covers model selection as well as parameter estimation simultaneously. RJMCMC can be applied when models contain different numbers of parameters. The algorithm is capable of moving between parameter spaces of different dimension in order to find the most appropriate model that describes the system and the most probable parameters within that model. In this contribution the RJMCMC algorithm is introduced in the context of nonlinear dynamical systems and is demonstrated on simulated data.