  In this paper, we investigate the problem of inverse electromagnetic
scattering to recover multilayer human tissue profiles using ultrawideband
radar systems in a Bayesian setting. We study the recovery problem in a blind
setting, in which we simultaneously estimate both the dielectric/geometric
properties of the one-dimensional target tissue profile and the transmitted
radar waveform. To perform Bayesian parameter estimation, we propose a hybrid
and adaptive Markov Chain Monte Carlo method, which combines the Slice sampling
and Hamiltonian Monte Carlo approaches. The introduced sampling mechanism also
incorporates the Parallel Tempering approach to escape from the local optimal
regions of the complex posterior distribution. We provide empirical support
through various numerical simulations for the achieved enhanced sampling
efficiency compared to conventional sampling schemes. To investigate the
recovery performance, we work on synthetic measurements simulating actual radar
returns from multilayer tissue profiles. We derive theoretical bounds for the
best achievable estimation performance in terms of normalized root mean square
error and provide a comparison with the performance of our estimator.
