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Axially symmetric models for global data: A journey between geostatistics and stochastic generators

Lookup NU author(s): Professor Emilio Porcu, Dr Alfredo Alegria Jimenez, Dr Paola Crippa

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


Abstract

© 2019 The Authors. Environmetrics Published by John Wiley & Sons Ltd. Decades of research in spatial statistics have prompted the development of a wide variety of models and methods whose primary goal is optimal linear interpolation (kriging), as well as sound assessment of the associated uncertainty (kriging variance). While kriging is of paramount importance for scientific investigations requiring high-resolution maps, spatial statistics can be used for other classes of applications as well. Indeed, new areas are emerging where the main goal is to simulate from a statistical model whose parameters have been estimated from the data. This paper focuses on two different ways to model global data with axially symmetric Gaussian processes, for which the covariance function is nonstationary over latitudes and stationary over longitudes. Both strategies are illustrated through a global data set on surface temperatures generated by the National Center for Atmospheric Research (NCAR). On the one hand, we downscale surface temperatures through a classical geostatistical approach. We exploit Gaussianity assumption to focus on the second-order structure, and we develop a novel class of axially symmetric models inspired from currently available isotropic models. We also propose a new covariance model that is axially symmetric. Covariance-based approaches are notorious for their computational burden, and a considerable amount of recent literature has been devoted to overcome this problem. We propose a simulation-based approach that works for processes defined on a lattice only. For such an approach, kriging cannot be performed as there is an underlying continuous process. At the same time, inference can be performed exactly on extremely large data sets.


Publication metadata

Author(s): Porcu E, Castruccio S, Alegria A, Crippa P

Publication type: Article

Publication status: Published

Journal: Environmetrics

Year: 2019

Volume: 30

Issue: 1

Print publication date: 01/02/2019

Online publication date: 10/01/2019

Acceptance date: 07/12/2018

Date deposited: 11/02/2019

ISSN (print): 1180-4009

ISSN (electronic): 1099-095X

Publisher: John Wiley and Sons Ltd

URL: https://doi.org/10.1002/env.2555

DOI: 10.1002/env.2555


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Funding

Funder referenceFunder name
1130647
1170290
FONDECYT 1130647

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