We present our recent results on Bayesian inversion for the WIPP groundwater flow problem.
In particular, we show how direct and indirect measurements of an unknown conductivity field can used to obtain a stochastic model for the unknown.
The main tool here is Bayes' theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements.
Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of polluting particles, can be obtained by Markov Chain Monte Carlo (MCMC) simulations.
Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.