Decomposition of Variance for Spatial Cox Processes

Abstract. Spatial Cox point processes is a natural framework for quantifying the various sources of variation governing the spatial distribution of rain forest trees. We introduce a general criterion for variance decomposition for spatial Cox processes and apply it to specific Cox process models with additive or log linear random intensity functions. We moreover consider a new and flexible class of pair correlation function models given in terms of normal variance mixture covariance functions. The proposed methodology is applied to point pattern data sets of locations of tropical rain forest trees.     

Residual Analysis for Inhomogeneous Neyman–Scott Processes

Abstract. In this article, we introduce a residual analysis for inhomogeneous Neyman–Scott models based on Laplace functionals. Our simulation study shows that this residual analysis method has a good performance in assessing goodness‐of‐fit and revealing inadequacy of the fitted model. The method is employed in fitting a Thomas model to California redwood trees data and a Matérn model to the locations of hickory trees in Lansing woods, Michigan.