Gaussian process regression in Bayesian inverse problems

 A major challenge in the application of sampling methods in Bayesian
inverse problems is the typically large computational cost associated
with solving the forward problem. To overcome this issue, we consider
using Gaussian process regression to approximate the forward map. This
results in an approximation to the solution of the Bayesian inverse
problem, and more precisely in an approximate posterior distribution.

In this talk, we analyse the error in the approximate posterior
distribution, and show that the approximate posterior distribution tends
to the true posterior as the accuracy of the Gaussian process emulator
increases.