Accelerated MCMC combining metamodel-based independent proposals and delayed rejection

Markov Chain Monte Carlo (MCMC) simulation has significant computational burden when evaluation of the associated target probability density function (PDF) involves a complex numerical model. A novel framework to accelerate MCMC is developed here for such applications. It leverages a metamodel approximation of the target PDF to improve computational efficiency, while preserves convergence properties to the exact target PDF, avoiding potential accuracy problems introduced through the metamodel error. This approach relies on the delayed-rejection (DR) scheme to combine rapid exploring global (independent) proposals with robust random walk proposals. A Kriging metamodel-based density approximation is chosen as the global proposal to generate candidate samples in each MCMC step. For any rejected sample, DR allows an extra random walk, avoiding potential issues when Kriging offers a poor approximation (i.e., underestimates) to the actual target PDF and guaranteeing convergence. The overall computational efficiency is further improved through adaptive Kriging updating during the MCMC sampling phase, by systematically including candidate samples who can substantially enhance Kriging's accuracy into the training database. The computational efficiency and robustness of the established algorithm is demonstrated in an analytical benchmark problem and an engineering Bayesian inference problem.