  Statistical modeling of presence-only data has attracted much recent
attention in the ecological literature, leading to a proliferation of methods,
including the inhomogeneous Poisson process (IPP) model, maximum entropy
(Maxent) modeling of species distributions and logistic regression models.
Several recent articles have shown the close relationships between these
methods. We explain why the IPP intensity function is a more natural object of
inference in presence-only studies than occurrence probability (which is only
defined with reference to quadrat size), and why presence-only data only allows
estimation of relative, and not absolute intensity of species occurrence. All
three of the above techniques amount to parametric density estimation under the
same exponential family model (in the case of the IPP, the fitted density is
multiplied by the number of presence records to obtain a fitted intensity). We
show that IPP and Maxent give the exact same estimate for this density, but
logistic regression in general yields a different estimate in finite samples.
When the model is misspecified - as it practically always is - logistic
regression and the IPP may have substantially different asymptotic limits with
large data sets. We propose ``infinitely weighted logistic regression,'' which
is exactly equivalent to the IPP in finite samples. Consequently, many
already-implemented methods extending logistic regression can also extend the
Maxent and IPP models in directly analogous ways using this technique.
