A Bayesian approach to crack detection in electrically conducting media

In this paper, we review powerful new computational techniques which facilitate the Bayesian approach to statistical inference and discuss how they may be used to solve general inverse problems. Their power and flexibility is illustrated by the problem of detecting a finite set of linear non-intersecting perfectly insulating cracks in a homogeneously electrically conducting medium. In this case, efficient algorithms only exist if the number of cracks is known a priori. However, in this paper we demonstrate how uncertainty about the number of cracks can be incorporated into the modelling process and assessed together with crack locations.