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Spatiotemporal models for skewed processes
Author(s) -
Schmidt Alexandra M.,
Gonçalves Kelly C. M.,
Velozo Patrícia L.
Publication year - 2017
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.2411
Subject(s) - transformation (genetics) , gaussian , gaussian process , interpolation (computer graphics) , bayesian inference , mathematics , bayesian probability , skewness , computer science , statistics , econometrics , artificial intelligence , motion (physics) , biochemistry , chemistry , physics , quantum mechanics , gene
In the analysis of most spatiotemporal processes in environmental studies, observations present skewed distributions. Usually, a single transformation of the data is used to approximate normality, and stationary Gaussian processes are assumed to model the transformed data. The choice of transformation is key for spatial interpolation and temporal prediction. We propose a spatiotemporal model for skewed data that does not require the use of data transformation. The process is decomposed as the sum of a purely temporal structure with two independent components that are considered to be partial realizations from independent spatial Gaussian processes, for each time t. The model has an asymmetry parameter that might vary with location and time, and if this is equal to zero, the usual Gaussian model results. The inference procedure is performed under the Bayesian paradigm, and uncertainty about parameters estimation is naturally accounted for. We fit our model to different synthetic data and to monthly average temperature observed between 2001 and 2011 at monitoring locations located in the south of Brazil. Different model comparison criteria and analysis of the posterior distribution of some parameters suggest that the proposed model outperforms standard ones used in the literature.