Local block bootstrap for inhomogeneous Poisson marked point processes

Local Block Bootstrap for Inhomogeneous Poisson Marked Point Processes

The asymptotic theory for the sample mean of a marked point process in d dimensions is established, allowing for the possibility that the underlying Poisson point process is inhomogeneous. A novel local block bootstrap method for resampling inhomogeneous Poisson marked point processes is introduced, and its consistency is proven for the sample mean and related statistics. Finite-sample simulati...

Technical supplement to : “ Local Block Bootstrap for Inhomogeneous Poisson Marked Point Processes ”

Summary statistics for inhomogeneous marked point processes

We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the n-point correlation functions and reduce to cross J and D-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions...

Fast Block Variance Estimation Procedures for Inhomogeneous Spatial Point Processes

We introduce two new variance estimation procedures by using non-overlapping and overlapping blocks, respectively. The non-overlapping block (NOB) estimator can be viewed as the limit of the thinned block bootstrap (TBB) estimator recently proposed in Guan and Loh (2007), by letting the number of thinned processes and bootstrap samples therein both increase to infinity. Compared to the latter, ...

Graphical Models for Marked Point Processes based on Local Independence

A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so–called local independencies, meaning that the intensities of certain types of events are independent of some (but not necessarilly all) events in the past. This dynamic concept of independence is asymmetric, similar to Granger non–causality, so that the correspond...