Hierarchical Bayesian Level Set Inversion Andrew Stuart University of Warwick I will begin by overviewing the Bayesian approach to the reconstruction of fields from indirect and noisy (possibly nonlinear) measurement functionals [1]. I will then explain the basic Bayesian level set approach to reconstructing piecewise constant fields [2]. Finally I will demonstrate how the method can be enhanced by means of a hierarchical multiscale approach in which the charateristic length scale of interface separation is learned from the data, along with the geometry of interfaces themselves. [1] M. Dashti and A.M. Stuart. The Bayesian approach to inverse problems. To appear in Handbook of Uncertainty Quantification, Springer, 2016. http://arxiv.org/abs/1302.6989 [2] M.A. Iglesias, Y. Lu, A.M. Stuart, "A level-set approach to Bayesian geometric inverse problems", submitted. http://arxiv.org/abs/1504.00313 Joint work with Matt Dunlop (Warwick) and Marco Iglesias (Nottingham)