FEM-based discretization-invariant MCMC methods for PDE-constrained Bayesian inverse problems
FEM-based discretization-invariant MCMC methods for PDE-constrained Bayesian inverse problems
We present a systematic construction of FEM-baseddimension-independent (discretization-invariant) Markov chain MonteCarlo (MCMC) approaches to explore PDE-constrained Bayesian inverseproblems in infinite dimensional parameter spaces. In particular, weconsider two frameworks to achieve this goal:Metropolize-then-discretize and discretize-then-Metropolize. Theformer refers to the method of discretizing function-space MCMCmethods. The latter, on the other hand, first …