On connected component Markov point processes

1999 ◽  
Vol 31 (02) ◽  
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.

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.

Markov point processes

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

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (3) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive scheme Xn = pXn-1 + ∊n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (03) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊ n } such that the sequence of random variables {X n } generated by the linear, additive first-order autoregressive scheme X n = pXn-1 + ∊ n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

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 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
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