A common approach to estimating the number of species in a taxonomic or other group is to extrapolate the temporal pattern of historical species discoveries or descriptions. A formal statistical approach to this problem is described. This approach involves fitting an explicit model of the discovery record by maximum likelihood and using the fitted model to estimate the number of undiscovered species. The approach is applied to a description record of large marine animals covering the period 1828-1996. The estimated number of undiscovered species in this group is around 10 with an upper 0.95 confidence bound of around 16.