The fundamental goal of mine detection is to achieve a high detection rate along with a low false alarm rate. While many mine detectors achieve the first of these goals, it is often at the cost of a prohibitively large false alarm rate. In this paper, a Bayesian decision-theoretic approach to the detection of mines, which incorporates the physical properties of the target response to an electromagnetic induction device, is presented. This approach merges physical modeling of the evoked target response with a probabilistic description that represents uncertainty in the ground surface, composition of the mine, and its placement in the surrounding environment. This approach provides both an optimal detection scheme, and performance evaluation measures in the form of probability of detection and false alarm rate. We present results in which the model-based, Bayesian approach significantly outperforms the energy detector and matched filter detectors on data obtained from the DARPA backgrounds clutter data collection experiment. In addition, the model-based, Bayesian approach is also shown to outperform a detector which estimates the eddy-current decay rate from the data. Results are also presented to illustrate the amount of sensitivity of the matched filter detector for a known environment to incorrect prior knowledge of uncertain parameters in the demining scenario, as well as the robustness of performance and performance bounds realizable by the optimum detection algorithm that properly accounts for uncertainty within a Bayesian framework.