Crudely, statistics can tell us how long we
should wait after a “last sighting” to be reasonably
sure that there will be no more sightings
and that we may consider the species extinct. A
sighting record consists of the times at which
individuals of a species were sighted. From a
statistical perspective, it is natural to model
a sighting record as a Poisson process with a
sighting rate that is positive up to the point of
extinction and 0 thereafter. Under this model,
the problem can be formulated as a test of the
null hypothesis that this sighting rate has not
yet fallen to 0 against the alternative hypothesis
that it has. Implicit in this formulation is that
the only way the sighting rate can fall to 0 is
for the species to become extinct. In practice,
the sighting rate will also fall to 0 if no effort
is made to see it. Here, we will assume that the
sighting effort is constant.