Random Marked Sets
TL;DR: In this article, the authors link random fields and marked point processes, and introduce a new class of stochastic processes which are defined on a random set in Road, where the mark covariance function of a random marked set is in general not positive definite.
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Abstract: We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in Rd. Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.
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Citations
Construction of Covariance Functions and Unconditional Simulation of Random Fields
Martin Schlather
- 01 Jan 2012
TL;DR: An overview over the approaches how models can be obtained in the classical approaches to geostatistics, for instance the turning bands and the random coins.
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Testing the random field model hypothesis for random marked closed sets
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Nonparametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets
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References
•Book
Image Analysis and Mathematical Morphology
Jean Serra
- 11 Feb 1984
TL;DR: This invaluable reference helps readers assess and simplify problems and their essential requirements and complexities, giving them all the necessary data and methodology to master current theoretical developments and applications, as well as create new ones.
10.1K
•Book
Stochastic Geometry and Its Applications
Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke +3 more
- 18 Jul 1996
TL;DR: Random Closed Sets I--The Boolean Model. Random Closed Sets II--The General Case.
4.7K
An introduction to the theory of point processes
Daryl J. Daley,David Vere-Jones +1 more
TL;DR: An introduction to the theory of point processes can be found in this article, where the authors introduce the concept of point process and point process theory and introduce point processes as a theory for point processes.
4.2K
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