Bayesian model calibration on active subspaces

For many applications, the calibration of model parameters is complicated by the fact that parameters are often unidentifiable in the sense that they are not uniquely determined by the data. Moreover, for problems with moderate parameter dimensions - e.g., 8-50 parameters - deterministic, frequentist, and Bayesian model calibration techniques will often stall or fail to converge. To address both problems, we consider model calibration on active subspaces comprised of linear combinations of parameters. We first discuss the construction of active subspaces for cases when gradients may or may not be available and note how one can compute global sensitivity indices. We then employ a Delayed Rejection Adaptive Metropolis algorithm to infer parameter distributions on the active subspace and then map these distributions back to the full space. We illustrate the technique for problems in which analytic solutions are available, discretized elliptic PDEs, and a closure relation employed in reactor design.