Bayesian Hierarchical Models can Infer Interpretable Predictions of Leaf Area Index From Heterogeneous Datasets

Environmental scientists often face the challenge of predicting a complex phenomenon from a heterogeneous collection of datasets that exhibit systematic differences. Accounting for these differences usually requires including additional parameters in the predictive models, which increases the probability of overfitting, particularly on small datasets. We investigate how Bayesian hierarchical models can help mitigate this problem by allowing the practitioner to incorporate information about the structure of the dataset explicitly. To this end, we look at a typical application in remote sensing: the estimation of leaf area index of white winter wheat, an important indicator for agronomical modeling, using measurements of reflectance spectra collected at different locations and growth stages. Since the insights gained from such a model could be used to inform policy or business decisions, the interpretability of the model is a primary concern. We, therefore, focus on models that capture the association between leaf area index and the spectral reflectance at various wavelengths by spline-based kernel functions, which can be visually inspected and analyzed. We compare models with three different levels of hierarchy: a non-hierarchical baseline model, a model with hierarchical bias parameter, and a model in which bias and kernel parameters are hierarchically structured. We analyze them using Markov Chain Monte Carlo sampling diagnostics and an intervention-based measure of feature importance. The improved robustness and interpretability of this approach show that Bayesian hierarchical models are a versatile tool for the prediction of leaf area index, particularly in scenarios where the available data sources are heterogeneous.