On a class of non-stationary, compactly supported spatial covariance functions

Globally supported covariance functions are generally associated with dense covariance matrices, meaning severe numerical problems in solution feasibility. These problems can be alleviated by considering methods yielding sparse covariance matrices. Indeed, having many zero entries in the covariance...

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Bibliographic Details
Published in:Stochastic environmental research and risk assessment 2013-02, Vol.27 (2), p.297-309
Main Authors: Mateu, J., Fernández-Avilés, G., Montero, J. M.
Format: Article
Language:English
Subjects:
Aquatic Pollution
Chemistry and Earth Sciences
Computational Intelligence
Computer Science
Earth and Environmental Science
Earth science
Earth Sciences
Environment
Environmental science
Math. Appl. in Environmental Science
Original Paper
Physics
Probability Theory and Stochastic Processes
Statistics for Engineering
Stochastic models
Storage requirements
Variance analysis
Waste Water Technology
Water Management
Water Pollution Control
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Summary:Globally supported covariance functions are generally associated with dense covariance matrices, meaning severe numerical problems in solution feasibility. These problems can be alleviated by considering methods yielding sparse covariance matrices. Indeed, having many zero entries in the covariance matrix can both greatly reduce computer storage requirements and the number of floating point operations needed in computation. Compactly supported covariance functions considerably reduce the computational burden of kriging, and allow the use of computationally efficient sparse matrix techniques, thus becoming a core aspect in spatial prediction when dealing with massive data sets. However, most of the work done in the context of compactly supported covariance functions has been carried out in the stationary context. This assumption is not generally met in practical and real problems, and there has been a growing recognition of the need for non-stationary spatial covariance functions in a variety of disciplines. In this paper we present a new class of non-stationary, compactly supported spatial covariance functions, which adapts a class of convolution-based flexible models to non-stationary situations. Some particular examples, computational issues, and connections with existing models are considered.
ISSN:1436-3240
1436-3259
DOI:10.1007/s00477-011-0510-8