The approximation error approach was proposed in [J. Kaipio \& E. Somersalo, Statistical and Computational Inverse Problems, Springer, 2004] for handling modelling errors due to model reduction and unknown nuisance parameters in inverse problems. In this talk, we discuss the application of the approximation error approach for approximate marginalization of modelling errors caused by inaccurately known sensor parameters in diffuse optical tomography. We also describe how the approximation error model can be employed for construction of surrogate models for computer simulations.