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arXiv · 2610.29365

Using Temporal Replication and Partial Pooling to Improve Practical Identifiability in Presence-Only Poisson Point Process Models

Camille Mottier·Iris Lang·Justine Nicolas·Olivier Gimenez
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Abstract

Species distribution models based on thinned point processes are now commonly used in ecology to analyze presence-only data collected through citizen science, including in spatio-temporal frameworks. A key challenge in these models is the separation of the ecological process from the observation process, which raises identifiability issues. Here, we investigate the theoretical and practical identifiability of a thinned Poisson point process model. We show that, with a log link for ecological intensity and a logit link for observation probability, the model can be structurally identifiable under simple conditions, provided that observation probability varies spatially. We then evaluate the benefits of using temporal replication within a spatio-temporal framework to improve estimation when ecological intensity and observation probability are weakly separated. We quantify these benefits through simulations. The results highlight persistent practical identifiability problems affecting the ecological and observation intercepts, especially when observation probabilities are low. However, in a spatio-temporal model with partial pooling, these parameters are estimated more accurately than in a single-year model, even when only a short time period is considered. Temporal replication also improves estimation of parameters shared across years. Finally, we illustrate the use of such a spatio-temporal model through a study of coypu (Myocastor coypus) distribution in Occitanie, France. Overall, our results show that temporal replication can partially alleviate practical identifiability problems in presence-only point process models when independent data sources are unavailable.

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Camille Mottier, Iris Lang, Justine Nicolas, Olivier Gimenez. 2026-10-21. Using Temporal Replication and Partial Pooling to Improve Practical Identifiability in Presence-Only Poisson Point Process Models. https://arxiv.org/abs/2610.29365

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