Bayesian System Identification of Dynamical Systems using Reversible Jump Markov Chain Monte Carlo

The purpose of this contribution is to illustrate the potential of Reversible Jump Markov Chain Monte Carlo (RJMCMC) methods for nonlinear system identification. Markov Chain Monte Carlo (MCMC) sampling methods have come to be viewed as a standard tool for tackling the issue of parameter estimation using Bayesian inference. A limitation of standard MCMC approaches is that they are not suited to tackling the issue of model selection. RJMCMC offers a powerful extension to standard MCMC approaches in that it allows parameter estimation and model selection to be addressed simultaneously. This is made possible by the fact that the RJMCMC algorithm is able to jump between parameter spaces of varying dimension. In this paper the background theory to the RJMCMC algorithm is introduced. Comparison is made to a standard MCMC approach.