The extinction of a species can be inferred from a record of its sightings. Existing methods for doing so assume that all sightings in the record are valid. Often, however, there are sightings of uncertain validity. To date, uncertain sightings have been treated in an ad hoc way, either excluding them from the record or including them as if they were certain. We developed a Bayesian method that formally accounts for such uncertain sightings. The method assumes that valid and invalid sightings follow independent Poisson processes and use noninformative prior distributions for the rate of valid sightings and for a measure of the quality of uncertain sightings. We applied the method to a recently published record of sightings of the Ivory-billed Woodpecker (Campephilus principalis). This record covers the period 1897-2010 and contains 39 sightings classified as certain and 29 classified as uncertain. The Bayes factor in favor of extinction was 4.03, which constitutes substantial support for extinction. The posterior distribution of the time of extinction has 3 main modes in 1944, 1952, and 1988. The method can be applied to sighting records of other purportedly extinct species.