  We consider the problem of local radioelectric property estimation from
global electromagnetic scattering measurements. This challenging ill-posed high
dimensional inverse problem can be explored by intensive computations of a
parallel Maxwell solver on a petaflopic supercomputer. Then, it is shown how
Bayesian inference can be perfomed with a Particle Marginal Metropolis-Hastings
(PMMH) approach, which includes a Rao-Blackwellised Sequential Monte Carlo
algorithm with interacting Kalman filters. Material properties, including a
multiple components "Debye relaxation"/"Lorenzian resonant" material model, are
estimated; it is illustrated on synthetic data. Eventually, we propose
different ways to deal with higher dimensional problems, from parallelization
to the original introduction of efficient sequential data assimilation
techniques, widely used in weather forecasting, oceanography, geophysics, etc.
