Properties of residuals for spatial point processes

Properties of Residuals for Spatial Point Processes

For any point process in R that has a Papangelou conditional intensity λ, we define a random measure of ‘innovations’ which has mean zero. When the point process model parameters are estimated from data, there is an analogous random measure of ‘residuals’. We analyse properties of the innovations and residuals, including first and second moments, conditional independence, a martingale property,...

Residuals and Diagnostics for Spatial Point Processes

Residuals for spatial point processes based on Voronoi tessellations

A residual analysis method for spatial point processes is proposed, where differences between the modeled conditional intensity and the observed number of points are assessed over the Voronoi cells generated by the observations. The resulting residuals appear to be substantially less skewed and hence more stable, particularly for point processes with conditional intensities close to zero, compa...

Filters for Spatial Point Processes

We study the general problem of estimating a ‘hidden’ point process X given the realisation of an ‘observed’ point process Y (possibly defined in different spaces) with known joint distribution. We characterise the posterior distribution of X under marginal Poisson and Gauss-Poisson prior and when the transformation from X to Y includes thinning, displacement and augmentation with extra points....

Computing point-set surfaces with controlled spatial variation of residuals

This paper presents an accurate method for computing point-set surfaces from input data that can suppress the noise effect in the resulting point-set surface. This is accomplished by controlling spatial variation of residual errors between the input data and the resulting point-set surface and offsetting any systematic bias. More specifically, this method first reduces random noise of input dat...