Parallel MCMC for Bayesian Inference in Inverse Scattering Problems

We present a new Parallel MCMC method for the solution of the Bayesian statistical inverse problem. Local Hessian and gradient information is used to adaptively construct a radial basis function approximation (RBF) of the posterior, which is used as proposal distribution for the Metropolis-Hastings algorithm across several parallel chains. Parallelism allows for rapid convergence of this approximation, and thus minimal sample correlation in the resulting MCMC chains.