Analyzing spatio-temporal data with R: Everything you always wanted to know – but were afraid to ask

RESSTE Network et al.

Journal de la société française de statistique, Tome 158 (2017) no. 3, pp. 124-158.

Nous présentons un aperçu des modèles, méthodes et techniques (géo-)statistiques pour l’analyse et la prévision de processus spatio-temporels continus. De nombreuses approches sont possibles pour la construction de modèles statistiques pour ces processus, l’estimation de leurs paramètres et leur prédiction. Nous avons choisi de présenter l’approche par processus gaussien, la plus communément utilisée en statistiques spatiales et en géostatistiques, ainsi que son implémentation avec le logiciel R. La variable cible est la moyenne de la concentration quotidienne PM${}_{10}$ à l’échelle de la France, prédite à l’aide d’un modèle de transport en chimie de l’atmosphère et de séries d’observations obtenues à des stations de surveillance de la qualité de l’air. En suivant le fil d’une application réelle de grande dimension, nous comparons certains des paquets R les plus utilisés. Le code R permettant la visualisation des données, l’estimation des paramètres de la fonction de covariance spatio-temporelle ainsi que la sélection d’un modèle et la prédiction de la concentration de PM${}_{10}$ est également présenté afin d’illustrer l’enchaînement des étapes. Nous concluons avec une comparaison entre les paquets qui sont disponibles aujourd’hui et ainsi que les pistes de développement qui nous paraissent intéressantes.

We present an overview of (geo-)statistical models, methods and techniques for the analysis and prediction of continuous spatio-temporal processes residing in continuous space. Various approaches exist for building statistical models for such processes, estimating their parameters and performing predictions. We cover the Gaussian process approach, very common in spatial statistics and geostatistics, and we focus on R-based implementations of numerical procedures. To illustrate and compare the use of some of the most relevant packages, we treat a real-world application with high-dimensional data. The target variable is the daily mean PM${}_{10}$ concentration predicted thanks to a chemistry-transport model and observation series collected at monitoring stations across France in 2014. We give R code covering the full work-flow from importing data sets to the prediction of PM${}_{10}$ concentrations with a fitted parametric model, including the visualization of data, estimation of the parameters of the spatio-temporal covariance function and model selection. We conclude with some elements of comparison between the packages that are available today and some discussion for future developments.

Keywords: Space-time, Covariance function, Geostatistics, Kriging, Air pollution
Mot clés : Fonction de covariance, Géostatistique, Krigeage, Pollution atmosphérique

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