Several new approaches to estimating the probability that a species is extinct have emerged recently. Different foundational assumptions can lead to different interpretations of data and potentially to different conclusions. To explore the implications of alternative formulations, here we develop and illustrate a Bayesian Updating method for inferring extinction based on records of observations and surveys. We illustrate how it combines incidental sightings and surveys with a data set for the Alaotra Grebe, showing how estimates of extinction may be updated as new data arise, providing a means for managers to reassess priorities for survey and management dynamically.