Inferring extinction date of a species using non-homogeneous Poisson processes with a change-point

Abstract

Bayesian methods have been developed for inferring the true year of extinction of a species from sighting records that have both certain and uncertain sightings. These methods typically make the restrictive assumption that all sighting types (i.e. certain, valid uncertain, invalid uncertain) derive from constant rate Poisson processes. In this study, the constant rate assumption in the homogeneous Poisson process is relaxed by allowing certain and uncertain sightings to follow independent non-homogeneous Poisson processes. The model can thus identify whether any of the sighting rates were increasing, decreasing or constant. In addition, a change-point is introduced to model the uncertain sig..