Abstract
The ubiquitous assumption of normality for modeling spatial and spatio-temporal data can be understood for many reasons. A major one is that the multivariate normal distribution is completely characterized by its first two moments. In addition, the stability of multivariate normal distribution under summation and conditioning offers tractability and simplicity. Gaussian spatial processes are well modeled and understood by the statistical and scientific communities, but for a wide range of environmental applications Gaussian spatial or spatio-temporal models cannot reasonably be fitted to the observations.
Keywords
- Covariance Function
- Gaussian Process
- Multivariate Normal Distribution
- Gaussian Vector
- Gaussian Random Process
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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- 1.
The logarithm of a bi-lognormal process is a process for which all univariate and bivariate marginals are Gaussian. It is thus a weaker assumption than the lognormality considered here.
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Acknowledgements
The author wishes to acknowledge Frédéric Baret, Sébastien Garrigues and Philippe Naveau, co-authors of some of the papers cited here. The research presented in Sect. 7.2.2 was funded by the ANR CLIMATOR project.
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Allard, D. (2012). Modeling Spatial and Spatio-Temporal Non Gaussian Processes. In: Porcu, E., Montero, J., Schlather, M. (eds) Advances and Challenges in Space-time Modelling of Natural Events. Lecture Notes in Statistics(), vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17086-7_7
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