Spatial kriging for replicated temporal point processes

Point processes , spatial – temporal

Estimation of summary characteristics from replicated spatial point processes

characteristics play an important role in the analysis of spatial point processes. We discuss various approaches to estimating summary characteristics from replicated observations of a stationary point process. The estimators are compared with respect to their integrated squared error. Simulations for three basic types of point processes help to indicate the best way of pooling the subwindow es...

Spatial and Spatio-temporal Point Processes

The present paper gives the background to point processes in space and time. Some special types of spatial and spatio-temporal models of point processes are introduced with the emphasis to Cox processes. Their basic properties are described and some characteristics are calculated. The simulation of one of these models is shown. Introduction At present, the theory of point processes is well esta...

Supplementary material for Independent Component Models for Replicated Point Processes

1 Estimation 1.1 EM algorithm We derive the EM algorithm for Uks withGamma( k; ) distributions, so S = Pp k=1 Uk isGamma( ; ) with = Pp k=1 k andW = U=S is Dirichlet( 1; : : : ; p), and S andW are independent. With a slight abuse of notation we are going to identify xB = ft1; : : : ; tmg with (m; t) from now on. The joint density of (m; t) and the latent variables (y; s;w) is f(m; t;y; s;w) = f...

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....