Intensity estimation for inhomogeneous Gibbs point process with covariates-dependent chemical activity

2014 ◽  
Vol 68 (3) ◽  
pp. 225-249
Author(s):  
Ondřej Šedivý ◽  
Antti Penttinen
Keyword(s):  
Point Process ◽  
Chemical Activity ◽  
Intensity Estimation ◽  
Gibbs Point Process

Gibbs point process models with mixed effects

2009 ◽  
Vol 21 (3-4) ◽  
pp. 341-353 ◽  
Author(s):  
Janine B. Illian ◽  
Ditte K. Hendrichsen
Keyword(s):  
Point Process ◽  
Mixed Effects ◽  
Process Models ◽  
Gibbs Point Process ◽  
Point Process Models

scholarly journals Bounds for the Probability Generating Functional of a Gibbs Point Process

2014 ◽  
Vol 46 (1) ◽  
pp. 21-34 ◽  
Author(s):  
Kaspar Stucki ◽  
Dominic Schuhmacher
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Upper Bounds ◽  
Pairwise Interaction ◽  
Summary Statistics ◽  
Lower And Upper Bounds ◽  
Generating Functional ◽  
Interaction Processes ◽  
Gibbs Point Process ◽  
Process Approximation

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.

Limit theorem and large deviation principle for the Voronoi tessellation generated by a Gibbs point process

1992 ◽  
Vol 24 (1) ◽  
pp. 45-70 ◽  
Author(s):  
Koji Kuroda ◽  
Hideki Tanemura
Keyword(s):  
Limit Theorem ◽  
Point Process ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Voronoi Tessellation ◽  
Deviation Principle ◽  
Gibbs Point Process ◽  
Polymer Expansion ◽  
Algebraic Formalism

The Voronoi tessellation generated by a Gibbs point process is considered. Using the algebraic formalism of polymer expansion, the limit theorem and the large deviation principle for the number of Voronoi vertices are proved.

scholarly journals Hybrids of Gibbs Point Process Models and Their Implementation

2013 ◽  
Vol 55 (11) ◽  
Author(s):  
Adrian Baddeley ◽  
Rolf Turner ◽  
Jorge Mateu ◽  
Andrew Bevan
Keyword(s):  
Point Process ◽  
Process Models ◽  
Gibbs Point Process ◽  
Point Process Models
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