Combining spatial transition probabilities for stochastic simulation of categorical fields
Journal
International Journal of Geographical Information Science
Date Issued
November 2011
DOI
10.1080/13658816.2010.528421
Abstract
Categorical spatial data, such as land use classes and socioeconomic statistics data, are
important data sources in geographical information science (GIS). The investigation of
spatial patterns implied in these data can benefit many aspects of GIS research, such
as classification of spatial data, spatial data mining, and spatial uncertainty modeling.
However, the discrete nature of categorical data limits the application of traditional
kriging methods widely used in Gaussian random fields. In this article, we present a
new probabilistic method for modeling the posterior probability of class occurrence at
any target location in space-given known class labels at source data locations within
a neighborhood around that prediction location. In the proposed method, transition
probabilities rather than indicator covariances or variograms are used as measures of
spatial structure and the conditional or posterior (multi-point) probability is approximated
by a weighted combination of preposterior (two-point) transition probabilities,
while accounting for spatial interdependencies often ignored by existing approaches. In
addition, the connections of the proposed method with probabilistic graphical models
(Bayesian networks) and weights of evidence method are also discussed. The advantages
of this new proposed approach are analyzed and highlighted through a case study
involving the generation of spatial patterns via sequential indicator simulation.
important data sources in geographical information science (GIS). The investigation of
spatial patterns implied in these data can benefit many aspects of GIS research, such
as classification of spatial data, spatial data mining, and spatial uncertainty modeling.
However, the discrete nature of categorical data limits the application of traditional
kriging methods widely used in Gaussian random fields. In this article, we present a
new probabilistic method for modeling the posterior probability of class occurrence at
any target location in space-given known class labels at source data locations within
a neighborhood around that prediction location. In the proposed method, transition
probabilities rather than indicator covariances or variograms are used as measures of
spatial structure and the conditional or posterior (multi-point) probability is approximated
by a weighted combination of preposterior (two-point) transition probabilities,
while accounting for spatial interdependencies often ignored by existing approaches. In
addition, the connections of the proposed method with probabilistic graphical models
(Bayesian networks) and weights of evidence method are also discussed. The advantages
of this new proposed approach are analyzed and highlighted through a case study
involving the generation of spatial patterns via sequential indicator simulation.