Mathematical simulation modelling of epidemic processes has recently become a popular tool in guiding policy decisions for potential disease outbreaks. Such models all rely on various parameters in order to specify quantities such as transmission and detection rates. However, the values of these parameters are peculiar to an individual outbreak, and estimating them in advance of an epidemic has been the major difficulty in the predictive credibility of such approaches. The obstruction to classical approaches in estimating model parameters has been that of missing data: (i) an infected individual is only detected after the onset of clinical signs, we never observe the time of infection directly; (ii) if we wish to make inference on an epidemic while it is in progress (in order to predict how it might unfold in the future), we must take into account the fact that there may be individuals who are infected but not yet detected. In this paper we apply a reversible-jump Markov chain Monte Carlo algorithm to a combined spatial and contact network model constructed in a Bayesian context to provide a real-time risk prediction during an epidemic. Using the example of a potential Avian H5N1 epidemic in the UK poultry industry, we demonstrate how such a technique can be used to give real-time predictions of quantities such as the probability of individual poultry holdings becoming infected, the risk that individual holdings pose to the population if they become infected, and the number and whereabouts of infected, but not yet detected, holdings. Since the methodology generalises easily to many epidemic situations, we anticipate its use as a real-time decision-support tool for targetting disease control to critical transmission processes, and for monitoring the efficacy of current control policy.