Abstract
We introduce a class of cox cluster processes called generalised shot noise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process that drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby, a very large class of models for aggregated or clustered point patterns is obtained. Due to the structure of GSNCPs, a number of useful results can be established. We focus first on deriving summary statistics for GSNCPs and, second, on how to simulate such processes. In particular, results on first- and second-order moment measures, reduced Palm distributions, the J-function, simulation with or without edge effects, and conditional simulation of the intensity function driving a GSNCP are given. Our results are exemplified in important special cases of GSNCPs, and we discuss their relation to the corresponding results for SNCPs.
Original language | English |
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Journal | Advances in Applied Probability |
Volume | 37 |
Issue number | 1 |
Pages (from-to) | 48-74 |
ISSN | 0001-8678 |
DOIs | |
Publication status | Published - 2005 |
Keywords
- Cluster process
- Conditional simulation
- Geometric ergodicity
- Metropolis-Hastings algorithm
- Spatial point process