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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-35
September 2000

A Bayesian Approach to Crack Detection in Electrically Conducting Media


Martin Bøgsted Hansen

Kim E. Andersen, Stephen P. Brooks


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 concucting media. 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 together with crack locations.

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This paper has now been published in Inverse Problems 17, 121-136.