Markov point processes for modeling of spatial forest patterns in Amazonia derived from interferometric height

2005 ◽  
Vol 97 (4) ◽  
pp. 484-494 ◽  
Author(s):  
Till Neeff ◽  
Gregory S. Biging ◽  
Luciano V. Dutra ◽  
Corina C. Freitas ◽  
João R. dos Santos
Keyword(s):  
Point Processes ◽  
Markov Point Processes

Markov point processes

1978 ◽  
Vol 10 (2) ◽  
pp. 262-263
Author(s):  
Erhan Çinlar
Keyword(s):  
Point Processes ◽  
Markov Point Processes

Transformations of Markov point processes

1998 ◽  
Vol 30 (2) ◽  
pp. 281-281
Author(s):  
Eva B. Vedel Jensen ◽  
Linda Stougaard Nielsen
Keyword(s):  
Point Processes ◽  
Markov Point Processes

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.

A spatial Markov property for nearest-neighbour Markov point processes

1990 ◽  
Vol 27 (04) ◽  
pp. 767-778 ◽  
Author(s):  
W. S. Kendall
Keyword(s):  
Point Processes ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Markov Point Processes

Nearest-neighbour Markov point processes were introduced by Baddeley and Møller (1989) as generalizations of the Markov point processes of Ripley and Kelly. This note formulates and discusses a spatial Markov property for these point processes.

Markov interacting component processes

2000 ◽  
Vol 32 (03) ◽  
pp. 597-619 ◽  
Author(s):  
Y. C. Chin ◽  
A. J. Baddeley
Keyword(s):  
Density Function ◽  
Point Processes ◽  
Characterization Theorem ◽  
Pairwise Interaction ◽  
Connected Components ◽  
Point Pattern ◽  
Component Process ◽  
Interaction Terms ◽  
Markov Point Processes ◽  
Component Processes

A generalization of Markov point processes is introduced in which interactions occur between connected components of the point pattern. A version of the Hammersley-Clifford characterization theorem is proved which states that a point process is a Markov interacting component process if and only if its density function is a product of interaction terms associated with cliques of connected components. Integrability and superpositional properties of the processes are shown and a pairwise interaction example is used for detailed exploration.

Compensator conditions for stochastic ordering of point processes

1991 ◽  
Vol 28 (04) ◽  
pp. 751-761 ◽  
Author(s):  
A. Kwieciński ◽  
R. Szekli
Keyword(s):  
Probability Space ◽  
Point Processes ◽  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Half Line ◽  
Simple Point ◽  
Martingale Approach ◽  
Random Elements ◽  
Markov Point Processes ◽  
Positive Half

Sufficient conditions are given under which two simple point processes on the positive half-line can be stochastically compared as random elements of D(0,∞) or R∞ + Using a martingale approach to point processes, the conditions are proposed via a compensator function family. Appropriate versions of the processes being compared are constructed on the same probability space. The results are illustrated by replacement policies and semi-Markov point processes.

On connected component Markov point processes

1999 ◽  
Vol 31 (2) ◽  
pp. 279-282 ◽  
Author(s):  
Y. C. Chin ◽  
A. J. Baddeley
Keyword(s):  
Point Processes ◽  
Connected Component ◽  
Wide Range ◽  
Markov Point Processes ◽  
Cluster Generation ◽  
Component Relation

We note some interesting properties of the class of point processes which are Markov with respect to the ‘connected component’ relation. Results in the literature imply that this class is closed under random translation and independent cluster generation with almost surely non-empty clusters. We further prove that it is closed under superposition. A wide range of examples is also given.

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