Bayesian inverse problem and optimization with iterative spatial resampling

摘要: [1] Measurements are often unable to uniquely characterize the subsurface at a desired modeling resolution. In particular, inverse problems involving characterization of hydraulic properties typically ill-posed since they generally present more unknowns than data. Bayesian context, solutions such consist posterior ensemble models that fit data (up certain precision specified by likelihood function) and subset prior distribution. Two possible approaches for this problem Markov chain Monte Carlo (McMC) techniques optimization (calibration) methods. Both frameworks rely on perturbation mechanism steer search solutions. When model parameters spatially dependent variable fields obtained using geostatistical realizations, as conductivity or porosity, it is not trivial incur perturbations respect spatial model. To overcome problem, we propose general transition kernel (iterative resampling, ISR) preserves any produced conditional simulation. We also stochastic stopping criterion optimizations inspired from importance sampling. studied cases, yields distributions reasonably close ones rejection sampler, but with greatly reduced number forward runs. The technique in sense can be used simulation method, whether generates continuous discrete variables. Therefore allows sampling different priors conditioning variety types. Several examples provided based either multi-Gaussian multiple-point statistics.