Bayesian System Identification of Nonlinear Dynamical Systems using a Fast MCMC Algorithm

This paper addresses the Bayesian parameter estimation of n onlinear, structurally dynamical systems. Specifically, i t is concerned with Markov Chain Monte Carlo (MCMC) methods wh ich, via the evolution of an ergodic Markov chain through the parameter space, allow one to generate samples from the post erior parameter distribution given by Bayes’ theorem. A ver sion of the well-known Simulated Annealing algorithm is presented whe re, to reduce computational cost, the transition from prior to posterior distributions is controlled via the gradual introduction o f data into the likelihood. A method is proposed which allows one to introduce data in a ‘smooth’ and continuous manner such that, while mov ing from prior to posterior, a constant change in Shannon ent ropy can be maintained. The performance of the algorithm is demonstr ated on the parameter estimation of a nonlinear dynamical sy stem.