A Bayesian approach to the prediction of occurred-but-not-yet-reported events is developed for application in real-time public health surveillance. The motivation was the prediction of the daily number of hospitalizations for the hemolytic-uremic syndrome during the large May–July 2011 outbreak of Shiga toxin-producing Escherichia coli (STEC) O104:H4 in Germany. Our novel Bayesian approach addresses the count data nature of the problem using negative binomial sampling and shows that right-truncation of the reporting delay distribution under an assumption of time-homogeneity can be handled in a conjugate prior-posterior framework using the generalized Dirichlet distribution. Since, in retrospect, the true number of hospitalizations is available, proper scoring rules for count data are used to evaluate and compare the predictive quality of the procedures during the outbreak. The results show that it is important to take the count nature of the time series into account and that changes in the delay distribution occurred due to intervention measures. As a consequence, we extend the Bayesian analysis to a hierarchical model, which combines a discrete time survival regression model for the delay distribution with a penalized spline for the dynamics of the epidemic curve. Altogether, we conclude that in emerging and time-critical outbreaks, nowcasting approaches are a valuable tool to gain information about current trends.