Efficient Discretization‐Independent Bayesian Inversion of High‐Dimensional Multi‐Gaussian Priors Using a Hybrid MCMC

In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations these fields, they discretized. Then, different techniques geostatistical inversion condition them on measurement data. Among techniques, Markov chain Monte Carlo (MCMC) stand out, because yield asymptotically unbiased conditional realizations. However, standard Chain methods suffer the curse dimensionality when refining discretization. This means that their efficiency decreases rapidly with an increasing number discretization cells. Several MCMC approaches have been developed such does not depend field. The preconditioned Crank Nicolson (pCN-MCMC) and sequential Gibbs (or block-Gibbs) sampling two examples. paper presents a combination both goal further reduce computational costs. Our algorithm, pCN-MCMC, will tuning-parameters: correlation parameter pCN approach block size approach. original pCN-MCMC algorithm special cases our method. We present automatically finds best tuning-parameter ( ) during burn-in-phase thus choosing possible hybrid between methods. test cases, we achieve speedup factors 1–5.5 over 1–6.5 Gibbs. Furthermore, provide MATLAB implementation method as open-source code.