This paper exploits the potential of a recently published multi-level MCMC algorithm, ABC-SubSim, for Bayesian inference of the model parameters of a general stochastic state-space model.

It is shown that the approximate posterior actually corresponds to an exact posterior under the assumption of the existence of uniformly-distributed measurement errors.

The original ABC-SubSim algorithm is improved by using an adaptive method to choose the proposal variance for the component-wise Metropolis algorithm.

Illustrative examples include the application of ABC-SubSim to Bayesian model updating of both linear and nonlinear dynamical systems.