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

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 sightings, where the sighting rates before and after the change-point vary. We have used Markov Chain Monte Carlo (MCMC) sampling to generate the posterior distributions for model parameters including species extinction time. The proposed method was applied to the sighting records of the black-footed ferret Mustela nigripes and the ivory-billed woodpecker Campephilus principalis (IBW) species. Based on a hypothesis test, the results of the model indicate that the species both went extinct in the years 1988 and 1956 respectively. Moreover, a decline in the certain sighting rate was also inferred for both these species, possibly indicating the decrease in the species abundance as it converges to extinction. Thus, earlier models that assume a constant sighting rate may well be biased. Uncertain sighting rates for the IBW were found to increase before extinction (indicating possibly some additional ecological attention received near extinction) and remained constant after extinction.