Practical Bayesian System Identification using Hamiltonian Monte Carlo

This paper addresses Bayesian system identification using a Markov Chain Monte Carlo approach. In particular, the Metroplis-Hastings algorithm with a Hamiltonian proposal - known as Hamiltonian Monte Carlo - is reviewed and adapted to linear and nonlinear system identification problems. The paper details how the Hamiltonian proposal can be arranged so that the associated Markov Chain performs well within the Metropolis-Hastings setting, which is a key practical challenge faced when using the latter approach for many system identification problems. This combination is demonstrated on several examples, ranging from simple linear to more complex nonlinear systems, on both simulated and real data.