Correcting for negative weights in ordinary kriging
Computers & Geosciences
Machine Learning
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
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This paper presents a general geostatistical framework for modeling categorical spatial data, an all important information source in many scientific fields. In the proposed framework, the multi-point class occurrence probability for (target) locations with unknown class labels given observed class labels at sample (source) locations is decomposed into a weighted combination of two-point spatial interactions in two different approaches, while accounting for complex spatial interdependencies. In the first approach, two-point spatial interactions are quantified directly by transiograms, a recently proposed set of spatial continuity measures in categorical fields. The sought-after multi-point class occurrence probability is then approximated based on a general paradigm (Tau model) for integrating knowledge from interdependent diverse information sources while accounting for information redundancy between them. In the second approach, geostatistical modeling of categorical spatial data is set in the framework of generalized linear mixed models (GLMMs), where latent spatially correlated Gaussian variables are assumed for the observable non-Gaussian responses to account for spatial correlation. Instead of using Markov Chain Monte Carlo sampling to infer the assumed latent variables, an ad-hoc method is proposed to approximate the analytically intractable posterior probability of the latent variables. The advantages of the new proposed framework are analyzed and highlighted through real and synthetic cases studies involving the generation of spatial patterns via sequential indicator simulation and interpolation of categorical spatial data.