scholarly journals The second-order analysis of stationary point processes

1976 ◽  
Vol 13 (02) ◽  
pp. 255-266 ◽  
Author(s):  
B. D. Ripley
Keyword(s):  
Stationary Point ◽  
Stochastic Geometry ◽  
Point Processes ◽  
Main Tool ◽  
Second Order ◽  
Spatial Point Processes ◽  
Order Analysis ◽  
Spatial Point ◽  
Moment Measures ◽  
Stationary Point Processes

This paper provides a rigorous foundation for the second-order analysis of stationary point processes on general spaces. It illuminates the results of Bartlett on spatial point processes, and covers the point processes of stochastic geometry, including the line and hyperplane processes of Davidson and Krickeberg. The main tool is the decomposition of moment measures pioneered by Krickeberg and Vere-Jones. Finally some practical aspects of the analysis of point processes are discussed.

scholarly journals The second-order analysis of stationary point processes

1976 ◽  
Vol 13 (2) ◽  
pp. 255-266 ◽  
Author(s):  
B. D. Ripley
Keyword(s):  
Stationary Point ◽  
Stochastic Geometry ◽  
Point Processes ◽  
Main Tool ◽  
Second Order ◽  
Spatial Point Processes ◽  
Order Analysis ◽  
Spatial Point ◽  
Moment Measures ◽  
Stationary Point Processes

This paper provides a rigorous foundation for the second-order analysis of stationary point processes on general spaces. It illuminates the results of Bartlett on spatial point processes, and covers the point processes of stochastic geometry, including the line and hyperplane processes of Davidson and Krickeberg. The main tool is the decomposition of moment measures pioneered by Krickeberg and Vere-Jones. Finally some practical aspects of the analysis of point processes are discussed.

θ-stationary point processes and their second-order analysis

1981 ◽  
Vol 18 (04) ◽  
pp. 864-878
Author(s):  
Karen Byth
Keyword(s):  
Point Process ◽  
Spatial Patterns ◽  
Stationary Point ◽  
Point Processes ◽  
Simulated Data ◽  
Second Order ◽  
Stationary Processes ◽  
Order Analysis ◽  
Stationary Point Processes ◽  
Point Of Reference

The concept of θ-stationarity for a simple second-order point process in R2 is introduced. This concept is closely related to that of isotropy. Some θ-stationary processes are defined. Techniques are given for simulating realisations of these processes. The second-order analysis of these processes which have an obvious point of reference or origin is considered. Methods are suggested for modelling spatial patterns which are realisations of such processes. These methods are illustrated using simulated data. The ideas are extended to multitype point processes.

θ-stationary point processes and their second-order analysis

1981 ◽  
Vol 18 (4) ◽  
pp. 864-878 ◽  
Author(s):  
Karen Byth
Keyword(s):  
Point Process ◽  
Spatial Patterns ◽  
Stationary Point ◽  
Point Processes ◽  
Simulated Data ◽  
Second Order ◽  
Stationary Processes ◽  
Order Analysis ◽  
Stationary Point Processes ◽  
Point Of Reference

The concept of θ-stationarity for a simple second-order point process in R2 is introduced. This concept is closely related to that of isotropy. Some θ-stationary processes are defined. Techniques are given for simulating realisations of these processes. The second-order analysis of these processes which have an obvious point of reference or origin is considered. Methods are suggested for modelling spatial patterns which are realisations of such processes. These methods are illustrated using simulated data. The ideas are extended to multitype point processes.

Second-Order Analysis of Inhomogeneous Spatial Point Processes Using Case-Control Data

Biometrics ◽  
2006 ◽  
Vol 63 (2) ◽  
pp. 550-557 ◽  
Author(s):  
P. J. Diggle ◽  
V. Gómez-Rubio ◽  
P. E. Brown ◽  
A. G. Chetwynd ◽  
S. Gooding
Keyword(s):  
Point Processes ◽  
Case Control ◽  
Second Order ◽  
Control Data ◽  
Spatial Point Processes ◽  
Order Analysis ◽  
Spatial Point

Some models for multitype spatial point processes, with remarks on analysing multitype patterns

1984 ◽  
Vol 21 (3) ◽  
pp. 575-582 ◽  
Author(s):  
H. W. Lotwick
Keyword(s):  
Point Processes ◽  
Empty Space ◽  
Second Order ◽  
Spatial Point Processes ◽  
Spatial Point ◽  
Methods Of Analysis ◽  
Second Order Methods

Two classes of ergodic stationary multitype spatial point processes are constructed. These processes have the property that interactions between the types exist, but cannot be detected using standard second-order methods of analysis. Simulations indicate that the interactions can, however, be detected by using ‘empty space' techniques.

Second‐order quasi‐likelihood for spatial point processes

Biometrics ◽  
2017 ◽  
Vol 73 (4) ◽  
pp. 1311-1320 ◽  
Author(s):  
Chong Deng ◽  
Yongtao Guan ◽  
Rasmus P. Waagepetersen ◽  
Jingfei Zhang
Keyword(s):  
Point Processes ◽  
Second Order ◽  
Spatial Point Processes ◽  
Spatial Point

Comparing the second-order properties of spatial point processes

2016 ◽  
Vol 9 (3) ◽  
pp. 365-374
Author(s):  
Azam Saadatjouy ◽  
Ali Reza Taheriyoun
Keyword(s):  
Point Processes ◽  
Second Order ◽  
Spatial Point Processes ◽  
Spatial Point
Sign in / Sign up

Export Citation Format

Share Document