A New Approach for Modelling Risk Dependence Using Spatial Point Processes

2011 ◽  
Author(s):  
Philip Pembe Umande
Keyword(s):  
Point Processes ◽  
Spatial Point Processes ◽  
New Approach ◽  
Spatial Point

scholarly journals Inhomogeneous spatial point processes by location-dependent scaling

2003 ◽  
Vol 35 (02) ◽  
pp. 319-336 ◽  
Author(s):  
Ute Hahn ◽  
Eva B. Vedel Jensen ◽  
Marie-Colette van Lieshout ◽  
Linda Stougaard Nielsen
Keyword(s):  
Point Processes ◽  
Spatial Point Processes ◽  
New Approach ◽  
Local Scaling ◽  
New Class ◽  
Spatial Point ◽  
New Process ◽  
Markov Point Processes ◽  
Global Scaling ◽  
Definition Of

A new class of models for inhomogeneous spatial point processes is introduced. These locally scaled point processes are modifications of homogeneous template point processes, having the property that regions with different intensities differ only by a scale factor. This is achieved by replacing volume measures used in the density with locally scaled analogues defined by a location-dependent scaling function. The new approach is particularly appealing for modelling inhomogeneous Markov point processes. Distance-interaction and shot noise weighted Markov point processes are discussed in detail. It is shown that the locally scaled versions are again Markov and that locally the Papangelou conditional intensity of the new process behaves like that of a global scaling of the homogeneous process. Approximations are suggested that simplify calculation of the density, for example, in simulation. For sequential point processes, an alternative and simpler definition of local scaling is proposed.

scholarly journals Inhomogeneous spatial point processes by location-dependent scaling

2003 ◽  
Vol 35 (2) ◽  
pp. 319-336 ◽  
Author(s):  
Ute Hahn ◽  
Eva B. Vedel Jensen ◽  
Marie-Colette van Lieshout ◽  
Linda Stougaard Nielsen
Keyword(s):  
Point Processes ◽  
Spatial Point Processes ◽  
New Approach ◽  
Local Scaling ◽  
New Class ◽  
Spatial Point ◽  
New Process ◽  
Markov Point Processes ◽  
Global Scaling ◽  
Definition Of

A new class of models for inhomogeneous spatial point processes is introduced. These locally scaled point processes are modifications of homogeneous template point processes, having the property that regions with different intensities differ only by a scale factor. This is achieved by replacing volume measures used in the density with locally scaled analogues defined by a location-dependent scaling function. The new approach is particularly appealing for modelling inhomogeneous Markov point processes. Distance-interaction and shot noise weighted Markov point processes are discussed in detail. It is shown that the locally scaled versions are again Markov and that locally the Papangelou conditional intensity of the new process behaves like that of a global scaling of the homogeneous process. Approximations are suggested that simplify calculation of the density, for example, in simulation. For sequential point processes, an alternative and simpler definition of local scaling is proposed.

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