Abstract
SummaryWe propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology thus develops high dimensional data understanding in the point process setting. The method is based on modelling the patterns by using a flexible Gibbs point process model to characterize point-to-point interactions at different spatial scales directly. By using the Gibbs framework significant interactions can also be captured at small scales. Subsequently, the Gibbs point process is fitted by using a pseudolikelihood approximation, and we select significant interactions automatically by using the group lasso penalty with this likelihood approximation. Thus we estimate the multivariate interactions stably even in this setting. We demonstrate the feasibility of the method with a simulation study and show its power by applying it to a large and complex rainforest plant population data set of 83 species.
Highlights
Spatial point patterns are a common form of observation in plant ecology (Waagepetersen et al, 2016), epidemiology (Diggle et al, 2005), astrophysics (Stoica et al, 2007), seismology (Schoenberg, 2003), social science (Amburgey, 1986), medicine (Olsbo et al, 2013) and criminology (Mohler et al, 2011)
Experiment 3 showed that the model can detect significant interactions in not just realizations of itself, and in realizations of Cox processes
We set the range vector equal across all 3486 intratype and intertype interactions and fitted the model twice, with range vector r = .7, 15/ m and with range vector r = .7, 15, 30/ m, the ranges being concordant with previous results of neighbourhood-dependent growth models within the Barro Colorado Island (BCI) forest (Table 4, Uriarte et al (2004))
Summary
Spatial point patterns are a common form of observation in plant ecology (Waagepetersen et al, 2016), epidemiology (Diggle et al, 2005), astrophysics (Stoica et al, 2007), seismology (Schoenberg, 2003), social science (Amburgey, 1986), medicine (Olsbo et al, 2013) and criminology (Mohler et al, 2011). The prevalence of multivariate point processes is noticeable in plant ecology where there may be many tens or hundreds of types (species) (Flugge et al, 2014; Baldeck et al, 2013a, b; Kanagaraj et al, 2011; Punchi-Manage et al, 2013). Such processes have seen much less study in the statistical literature than univariate processes and present some novel challenges, as we shall explain and address in this paper.
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