This thesis considers analysis of magnetic and electromagnetic data for the purpose of discriminating between buried unexploded ordnance (UXO) and non-hazardous metallic clutter. Magnetic data acquired over a ferrous object are modelled as a magnetostatic dipole. For time-domain electromagnetic data, a linear combination of decaying, orthogonal dipoles represents the secondary magnetic field radiated by a conductor. Model parameters estimated with inversion can be input into a discrimination algorithm whose output is a ranked diglist of targets. Algorithms that have been applied to UXO discrimination can be broadly categorized as library or statistical methods. Library methods assume that for each ordnance type there is a single set of parameters which is representative of intrinsic target properties. Statistical methods try to formulate a decision rule with a training set of models for targets with known ground truth. Observed data can sometimes have non-normally distributed noise and consequently parameter estimates obtained via least squares inversion may be biased. Robust misfit functions provide improved estimates of model parameters when there are outliers in the data. I also investigate propagation of uncertainties from data to model parameters. For inversion of electromagnetic data I find that parameters derived from the dipole model are approximately normally distributed. However, when data coverage is poor or SNR is low, the posterior distribution of these parameters may be multimodal. I develop a statistical classification algorithm that incorporates parameter uncertainty by integrating over the posterior probability distribution. Simulations and applications to real data indicate that this technique can detect outliers to the distribution of ordnance sooner than conventional classifiers. I quantify the performance of a discrimination algorithm using metrics derived from the receiver operating characteristic (ROC) curve. I use a bootstrapping algorithm to.