Active disease surveillance during epidemics is of utmost importance in detecting and eliminating new cases quickly, and targeting such surveillance to high-risk individuals is considered more efficient than applying a random strategy. Contact tracing has been used as a form of at-risk targeting, and a variety of mathematical models have indicated that it is likely to be highly efficient. However, for fast-moving epidemics, resource constraints limit the ability of the authorities to perform, and follow up, contact tracing effectively. As an alternative, we present a novel real-time Bayesian statistical methodology to determine currently undetected (occult) infections. For the UK foot-and-mouth disease (FMD) epidemic of 2007, we use real-time epidemic data synthesized with previous knowledge of FMD outbreaks in the UK to predict which premises might have been infected, but remained undetected, at any point during the outbreak. This provides both a framework for targeting surveillance in the face of limited resources and an indicator of the current severity and spatial extent of the epidemic. We anticipate that this methodology will be of substantial benefit in future outbreaks, providing a compromise between targeted manual surveillance and random or spatially targeted strategies.