Hierarchical log Gaussian Cox process for regeneration in uneven-aged forests

We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points x affects another set of points y but not vice versa. We use the model to investigate the effect of large trees to the locations of seedlings. In the model, every point in x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The par…

Estimation of forest stand characteristics using individual tree detection, stochastic geometry and a sequential spatial point process model

Airborne Laser Scanning (ALS) results in point-wise measurements of canopy height, which can further be used for Individual Tree Detection (ITD). However, ITD cannot find all trees because small trees can hide below larger tree crowns. Here we discuss methods where the plot totals and means of tree-level characteristics are estimated in such context. The starting point is a previously presented Horvitz–Thompson-like (HT-like) estimator, where the detectability is based on the larger tree crowns and a tuning parameter that models the detection condition. We propose a new method which is based on modeling the spatial pattern of hidden tree locations using a sequential spatial point process mo…

Statistical models and inference for spatial point patterns with intensity-dependent marks

Conditionally heteroscedastic intensity-dependent marking of log Gaussian Cox processes

Spatial marked point processes are models for systems of points which are randomly distributed in space and provided with measured quantities called marks. This study deals with marking, that is methods of constructing marked point processes from unmarked ones. The focus is density-dependent marking where the local point intensity affects the mark distribution. This study develops new markings for log Gaussian Cox processes. In these markings, both the mean and variance of the mark distribution depend on the local intensity. The mean, variance and mark correlation properties are presented for the new markings, and a Bayesian estimation procedure is suggested for statistical inference. The p…