  This paper considers Bayesian parameter estimation of dynamic systems using a
Markov Chain Monte Carlo (MCMC) approach. The Metroplis-Hastings (MH) algorithm
is employed, and the main contribution of the paper is to examine and
illustrate the efficacy of a particular proposal density based on energy
preserving Hamiltonian dynamics, which results in what is known in the
statistics literature as ``Hamiltonian Monte--Carlo'' (HMC). The very
significant utility of this approach is that, as will be illustrated, it
greatly reduces (almost to the point of elimination) the typically very high
correlation in the Metropolis--Hastings chain which has been observed by
several authors to restrict the application of the MH approach to only very low
dimension model structures. The paper illustrates how the HMC approach may be
applied to both significant dimension linear and nonlinear model structures,
even when the system order is unknown, and using both simulated and real data.
