scholarly journals Fast Covariance Estimation for Innovations Computed from a Spatial Gibbs Point Process

2013 ◽  
Vol 40 (4) ◽  
pp. 669-684 ◽  
Author(s):  
Jean-François Coeurjolly ◽  
Ege Rubak
Keyword(s):  
Point Process ◽  
Covariance 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

scholarly journals Gibbs Point Process Model for Young Star Clusters in M33

2020 ◽  
Author(s):  
Dayi Li ◽  
Pauline Barmby
Keyword(s):  
Point Process ◽  
Process Model ◽  
Function Analysis ◽  
Cluster Formation ◽  
Process Models ◽  
Spatial Distributions ◽  
Galactocentric Distance ◽  
Stellar Cluster ◽  
Positive Effects ◽  
Gibbs Point Process

Abstract We demonstrate the power of Gibbs point process models from the spatial statistics literature when applied to studies of resolved galaxies. We conduct a rigorous analysis of the spatial distributions of objects in the star formation complexes of M33, including giant molecular clouds (GMCs) and young stellar cluster candidates (YSCCs). We choose a hierarchical model structure from GMCs to YSCCs based on the natural formation hierarchy between them. This approach circumvents the limitations of the empirical two-point correlation function analysis by naturally accounting for the inhomogeneity present in the distribution of YSCCs. We also investigate the effects of GMCs’ properties on their spatial distributions. We confirm that the distribution of GMCs and YSCCs are highly correlated. We found that the spatial distributions of YSCCs reaches a peak of clustering pattern at ∼250 pc scale compared to a Poisson process. This clustering mainly occurs in regions where the galactocentric distance ≳ 4.5 kpc. Furthermore, the galactocentric distance of GMCs and their mass have strong positive effects on the correlation strength between GMCs and YSCCs. We outline some possible implications of these findings for our understanding of the cluster formation process.

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