We describe a method for calculating 95 per cent bounds for the current number of hidden cases and the future number of diagnosed cases during an outbreak of an infectious disease. A Bayesian Markov chain Monte Carlo approach is used to fit a model of infectious disease transmission that takes account of undiagnosed cases. Assessing this method on simulated data, we find that it provides conservative 95 per cent bounds for the number of undiagnosed cases and future case numbers, and that these bounds are robust to modifications in the assumptions generating the simulated data. Moreover, the method provides a good estimate of the initial reproduction number, and the reproduction number in the latter stages of the outbreak. Applying the approach to SARS data from Hong Kong, Singapore, Taiwan and Canada, the bounds on future diagnosed cases are found to be reliable, and the bounds on hidden cases suggests that there were few hidden cases remaining at the end of the outbreaks in each region. We estimate that the initial reproduction numbers lay between 1.5 and 3, and the reproduction numbers in the later stages of the outbreak lay between 0.36 and 0.6. Copyright © 2006 John Wiley & Sons, Ltd.