Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates

• Nested sampling (NS) is proposed for Bayesian prior model selection.
• The NS algorithm is accelerated using a two-stage MCMC sampling.
• A response surface is built for cheap evaluation of approximate likelihood function.
• Nested sampling is applied for calibration of several subsurface flow problems.

An efficient Bayesian calibration method based on the nested sampling (NS) algorithm and non-intrusive polynomial chaos method is presented. Nested sampling is a Bayesian sampling algorithm that builds a discrete representation of the posterior distributions by iteratively re-focusing a set of samples to high likelihood regions. NS allows representing the posterior probability density function (PDF) with a smaller number of samples and reduces the curse of dimensionality effects. The main difficulty of the NS algorithm is in the constrained sampling step which is commonly performed using a random walk Markov Chain Monte-Carlo (MCMC) algorithm. In this work, we perform a two-stage sampling using a polynomial chaos response surface to filter out rejected samples in the Markov Chain Monte-Carlo method. The combined use of nested sampling and the two-stage MCMC based on approximate response surfaces provides significant computational gains in terms of the number of simulation runs. The proposed algorithm is applied for calibration and model selection of subsurface flow models.