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Bayesian inversion approaches may be useful for inferring metallic scatterer shapes, and thereby assist in discriminating buried unexploded ordnance (UXO). The fundamental feature of Bayesian inversion is its attempt at rational incorporation of prior information in the inference algorithm. In UXO detection and classification, the model is a set of parameters corresponding to a particular object in a particular disposition. Prior information about the target sought and the randomness of noise and clutter from different sources warrant the application of a Bayesian approach. Broadband electromagnetic induction (EMI) responses at different locations, in terms of scattered magnetic field components in-phase and out-of-phase with the transmitted primary field, form the data vector. Here a fast forward model, in which we successfully represent a steel cylinder by a spheroid, is exploited for inversion computations. The validated model produces synthetic data, for which Bayesian inversion is compared to simple least squares (SLS), i.e. without weighting or damping. The Bayesian approach can provide more accurate results, if we can provide reasonable prior information.