MVGA Cox Processes

When modelling spatial point pattern data, we often have to account for either non-stationarity or anisotropy (or both) – essentially, allowing for the statistical properties of the data to vary with translations or rotations of the observation window.

Geometric anisotropic Cox processes [1] are great for modelling point patterns with directional clusters (i.e. those that display rotational heterogeneity). This is particularly useful in ecological modelling, for instance in replicating clusters of trees in a forest, where directionality can arise due to environmental factors, such as the presence of a river, or a prevailing wind that aids seed dispersal.

So far, this methodology has been restricted to univariate point patterns (e.g. a single tree species). In this work, we show how to include anisotropy in the joint dependence of a multivariate log-Gaussian Cox process. This allows us to model e.g. pairs of species where the interspecific dependence is directional. This relationship has been observed in nurse-plant relationships, where one species (the 'nurse') gives cover to another species whilst the latter is in their seedling/juvenile stages.

We give conditions under which a multivariate LGCP (driven by a Matérn covariance function) can display multivariate anisotropy, and we develop methods for estimating both the anisotropy and covariance parameters. We also demonstrate our model on two species in the widely-studied BCI tropical forest data, successfully replicating between-species anisotropy where an otherwise-equivalent isotropic model fails to do so!