Calibrate, emulate, sample

Many parameter estimation problems arising in applications can be cast the framework of Bayesian inversion. This allows not only for an estimate parameters, but also quantification uncertainties estimates. Often such parameter-to-data map is very expensive to evaluate, and computing derivatives map, or derivative-adjoints, may feasible. Additionally, many noisy evaluations available. We propose approach inversion settings that builds on derivative-free optimization capabilities ensemble Kalman methods. The overarching first use sampling (EKS) calibrate unknown parameters fit data; second, output EKS emulate map; third, sample from approximate posterior distribution which replaced by its emulator. results a principled inference requires small number (possibly approximation the) map. It does require this instead leverages documented power Furthermore, has desirable property it evolves towards regions bulk mass located, thereby locating them well emulation phase methodology. In essence, methodology provides cheap solution design problem where place points space efficiently train emulator purposes