Bayesian selection of mixed covariates from a latent layer: application to hierarchical modeling of soil carbon dynamics

Jreich, Rana; Hatte, Christine; Balesdent, Jérôme; Parent, Éric

Journal de la société française de statistique, Tome 159 (2018) no. 2, pp. 128-155.

Le carbone du sol est important non seulement pour assurer la sécurité alimentaire en maintenant la fertilité des sols, mais aussi pour limiter le réchauffement climatique en augmentant la séquestration du carbone dans le sol. Il est urgent de comprendre la réaction du carbone du sol face au réchauffement climatique et au changement des pratiques agricoles. Des modèles bio-physiques ont été développés depuis quelques décennies pour étudier la matière organique du sol (SOM). Cependant, il existe encore une forte incertitude sur les mécanismes contrôlant la dynamique de la SOM, du niveau microbien aux échelles globales. Dans cet article, nous proposons une approche statistique bayésienne de sélection de variables pour mieux cerner la dynamique du carbone du sol en examinant la variation en profondeur du radiocarbone pour 159 profils sous différentes conditions de climat (température, précipitations, ...) et d’environnement (type de sol, type d’usage du sol, ...). La recherche stochastique de sélection de variables (SSVS) est appliquée au niveau des variables latentes d’un modèle bayésien hiérarchique. Ce modèle décrit la variation du radiocarbone en fonction de la profondeur et en tenant compte des covariables explicatives potentielles tels que les facteurs climatiques et environnementaux. Cette approche nous permet d’avoir un jugement probabiliste sur la contribution conjointe du type de sol, du climat et de l’usage du sol à la dynamique verticale du carbone dans le sol. Nous discutons également de la performance pratique et des limitations de SSVS en présence de covariables catégorielles et de la colinéarité entre certaines covariables quand elles interviennent au niveau d’une couche latente d’un modèle bayésien hiérarchique.

Soil carbon is important not only to ensure food security via soil fertility, but also to potentially mitigate global warming via increasing soil carbon sequestration. There is an urgent need to understand the response of the soil carbon pool to climate change and agricultural practices. Biophysical models have been developed to study Soil Organic Matter (SOM) for some decades. However, there still remains considerable uncertainty about the mechanisms that affect SOM dynamics from the microbial level to global scales. In this paper, we propose a statistical Bayesian selection approach to study which forcing conditions influence soil carbon dynamics by looking at the depth distribution of radiocarbon content for 159 profiles under different conditions of climate (temperature, precipitation, etc.) and environment (soil type, land-use). Stochastic Search Variable Selection (SSVS) is here applied to latent variables in a hierarchical Bayesian model. The model describes variations of radiocarbon content as a function of depth and potential covariates such as climatic and environmental factors. SSVS provides a probabilistic judgment about the joint contribution of soil type, climate and land use on soil carbon dynamics. We also discuss the practical performance and limitations of SSVS in presence of categorical covariates and collinearity between covariates in the latent layers of the model.

Keywords: Bayesian selection approach, SSVS, spike and slab prior, hierarchical Bayesian model, latent variables, organic carbon dynamics, radiocarbon
Mot clés : méthode bayésienne de sélection de variables, recherche stochastique de sélection de covariables, modèle hiérarchique bayésien, variables latentes, ynamique du carbone organique, radiocarbone

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