Multilevel MCMC with Level-Dependent Data in a Model Case of Structural Damage Assessment

We discuss a generalisation of the multilevel Markov Chain Monte Carlo algorithm for a Bayesian inverse problem with high-resolution (full-field) data. We extend the method to include a level-dependent treatment of the data, which is useful for very high-resolution data that cannot be represented by the much lower resolution of the forward problem at coarser levels. The approach is illustrated using a model case situated in a context of structural health monitoring, additionally providing a new application domain for the multilevel Markov Chain Monte Carlo methodology.