Sampling informative/complex a priori probability distributions using Gibbs sampling assisted by sequential simulation

Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis algorithm can be used to sample the solutions to non-linear inverse problems. In principle these methods allow incorporation of arbitrarily complex a priori information, but current methods allow only relatively simple priors to be used. We demonstrate how sequential simulation can be seen as an application of the Gibbs sampler, and how such a Gibbs sampler assisted by sequential simulation can be used to perform a random walk generating realizations of a relatively complex random function. We propose to combine this algorithm with the Metropolis algorithm to obtain an efficient method for sampling posterior probability densities for nonlinear inverse problems.