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**Poisson point process models solve the “pseudo-absence problem” for presence-only data in ecology.**
*(English)*
Zbl 1202.62171

Ann. Appl. Stat. 4, No. 3, 1383-1402 (2010); correction ibid. 4, No. 4, 2203-2204 (2010).

Summary: Presence-only data, point locations where a species has been recorded as being present, are often used in modeling the distribution of a species as a function of a set of explanatory variables, whether to map species occurrence, to understand its association with the environment, or to predict its response to environmental change. Currently, ecologists most commonly analyze presence-only data by adding randomly chosen “pseudo-absences” to the data such that it can be analyzed using logistic regression, an approach which has weaknesses in model specification, in interpretation, and in implementation. To address these issues, we propose Poisson point process modeling of the intensity of presences. We also derive a link between the proposed approach and logistic regression, specifically, we show that as the number of pseudo-absences increases (in a regular or uniform random arrangement), logistic regression slope parameters and their standard errors converge to those of the corresponding Poisson point process model. We discuss the practical implications of these results. In particular, point process modeling offers a framework for choice of the number and location of pseudo-absences, both of which are currently chosen by ad hoc and sometimes ineffective methods in ecology, a point which we illustrate by example.

### MSC:

62P12 | Applications of statistics to environmental and related topics |

60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |

62J12 | Generalized linear models (logistic models) |

65C60 | Computational problems in statistics (MSC2010) |

### Keywords:

habitat modeling; quadrature points; occurrence data; pseudo-absences; species distribution modeling
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\textit{D. I. Warton} and \textit{L. C. Shepherd}, Ann. Appl. Stat. 4, No. 3, 1383--1402 (2010; Zbl 1202.62171)

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