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

摘要

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