Abstract: We are concerned with a novel Bayesian statistical framework for the characterization of natural subsurface formations, a very challenging task. Because of the large dimension of the stochastic space of the prior distribution in the framework, typically a dimensional reduction method, such as a Karhunen-Loeve expansion (KLE), needs to be applied to the prior distribution to make the characterization computationally tractable. Due to the large variability of properties of subsurface formations (such as permeability and porosity) it may be of value to localize the sampling strategy so that it can better adapt to large local variability of rock properties. We introduce the concept of multiscale sampling to localize the search in the stochastic space. The localization of the search is performed by multiscale blocking, and we apply a KL expansion locally, at the subdomain level. The effectiveness of the proposed framework is tested in the solution of inverse problems related to elliptic partial differential equations and single-phase porous media flows. We use multi-chain studies to show that the new algorithm clearly improves the convergence rate of the preconditioned MCMC method.