For O a bounded domain in Rd and a given smooth
function g:O→R, we consider the statistical nonlinear
inverse problem of recovering the conductivity f>0 in the divergence form
equation ∇⋅(f∇u)=gonO,u=0on∂O, from N discrete noisy point
evaluations of the solution u=uf on O. We study the statistical
performance of Bayesian nonparametric procedures based on a flexible class of
Gaussian (or hierarchical Gaussian) process priors, whose implementation is
feasible by MCMC methods. We show that, as the number N of measurements
increases, the resulting posterior distributions concentrate around the true
parameter generating the data, and derive a convergence rate N−λ,λ>0, for the reconstruction error of the associated posterior means, in
L2(O)-distance