Robust variable selection for spatial point processes observed with noise
This addresses the challenge of identifying spatial covariates in noisy data for fields like ecology and remote sensing, but it is incremental as it builds on existing sparse estimation and stability selection techniques.
The authors tackled the problem of variable selection in spatial point processes affected by noise, such as from remote sensing, by proposing a method combining sparsity-promoting estimation with noise-robust model selection, and demonstrated in simulations that it reliably recovers true covariates and improves selection accuracy and stability.
We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available through remote sensing and automated image analysis, identifying spatial covariates that influence the localization of events is crucial to understand the underlying mechanism. However, results from automated acquisition techniques are often noisy, for example due to measurement uncertainties or detection errors, which leads to spurious displacements and missed events. We study the impact of such noise on sparse point-process estimation across different models, including Poisson and Thomas processes. To improve noise robustness, we propose to use stability selection based on point-process subsampling and to incorporate a non-convex best-subset penalty to enhance model-selection performance. In extensive simulations, we demonstrate that such an approach reliably recovers true covariates under diverse noise scenarios and improves both selection accuracy and stability. We then apply the proposed method to a forestry data set, analyzing the distribution of trees in relation to elevation and soil nutrients in a tropical rain forest. This shows the practical utility of the method, which provides a systematic framework for robust variable selection in spatial point-process models under noise, without requiring additional knowledge of the process.