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Bayesian cross-validation of geostatistical models
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Lobo, Viviana G. R., Fonseca, Thaís C. O. and Fernando, A. S. Moura (2020) Bayesian cross-validation of geostatistical models. Spatial Statistics, 35 . 100394. doi:10.1016/j.spasta.2019.100394 ISSN 2211-6753.
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Official URL: https://doi.org/10.1016/j.spasta.2019.100394
Abstract
The problem of validating or criticizing models for georeferenced data is challenging as much as conclusions may be sensitive to the partition of data into training and validation cases. This is an obvious issue related to the basic validation scheme which selects a subset of the data to leave out of estimation and to make predictions with an assumed model. In this setup, only a few out-of-sample locations are usually selected to validate the model. On the other hand, the cross-validation approach, which considers several possible configurations of data divided into training and validation observations, is an appealing alternative, but it could be computationally demanding as the estimation of parameters usually requires computationally intensive methods. The purpose of this work is to use cross-validation techniques to choose between competing models and to assess the goodness of fit of spatial models in different regions of the spatial domain. We consider the sampling design for selecting the training and validation sets by assigning a probability distribution to the possible data partitions. To deal with the computational burden of cross-validation, we estimate discrepancy functions in a computationally efficient manner based on the importance weighting of posterior samples. Furthermore, we propose a stratified cross-validation scheme to take into account spatial heterogeneity, reducing the total variance of estimated predictive discrepancy measures. We also illustrate the advantages of our proposal with simulated examples of homogeneous and inhomogeneous spatial processes and with an application to rainfall dataset in Rio de Janeiro.
The purpose of this work is to use cross-validation techniques to choose between competing models and to assess the goodness of fit of spatial models in different regions of the spatial domain. We consider the sampling design for selecting the training and validation sets by assigning a probability distribution to the possible data partitions. To deal with the computational burden of cross-validation, we estimate discrepancy functions in a computationally efficient manner based on the importance weighting of posterior samples. Furthermore, we propose a stratified cross-validation scheme to
take into account spatial heterogeneity, reducing the total variance of estimated predictive discrepancy measures. We also illustrate the advantages of our proposal with simulated examples of homogeneous and inhomogeneous spatial processes and with an application to rainfall dataset in Rio de Janeiro.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Stochastic processes, Spatial analysis (Statistics), Bayesian statistical decision theory | |||||||||
Journal or Publication Title: | Spatial Statistics | |||||||||
Publisher: | Elsevier B.V. | |||||||||
ISSN: | 2211-6753 | |||||||||
Official Date: | March 2020 | |||||||||
Dates: |
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Volume: | 35 | |||||||||
Article Number: | 100394 | |||||||||
DOI: | 10.1016/j.spasta.2019.100394 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 28 November 2019 | |||||||||
Date of first compliant Open Access: | 14 November 2020 | |||||||||
RIOXX Funder/Project Grant: |
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