Hierarchical Bayesian Generalized Linear Models for Predicting Stagonospora Nodorum Blotch in Winter Wheat. Part I: Model Development and Evaluation

Reliable and uncertainty calibrated prediction of plant disease epidemics are key for informing disease management decisions. Such performance can be attained through hierarchical models designed to integrate field-level management data with higher-level environmental processes that drive epidemic development. In this study, a Bayesian hierarchical framework employing Beta regression was developed and validated to predict severity of Stagonospora nodorum blotch (SNB) in winter wheat. Nine competing models (M1–M9) combined individual-level management covariates (residue management, cultivar reaction class, disease onset) with group-level predictors derived from up to 117 pre-anthesis weather variables, a key biofix for fungicide decision-making. Inference for this high dimensional weather dataset, generated through window-pane analysis and factor analytic environmental loadings, was stabilized with R2D2 shrinkage priors. The full model (M9; 3 categorical + 117 weather predictors) achieved the highest accuracy ( RMSE : 3.6%, MAE : 3.1%) and outperformed an XGBoost benchmark ( RMSE : 4.6%). A more parsimonious model (M7; 3 categorical + 42 weather predictors) retained interpretability while maintaining robust performance ( RMSE : 3.9%, MAE : 3.2%). Predictive intervals were well-calibrated ( PICP ≈ 97%), but models slightly under-predicted severe epidemics (>15% severity), likely reflecting the constraints of relying exclusively on pre-anthesis weather in the absence of pathogen data. Simulations probing model behavior revealed how asymptote bias and coefficient uncertainty are influenced by group-effect variability, environmental relatedness, and sample size. These results demonstrate that uncertainty aware hierarchical models can resolve the multi scale drivers of SNB, and thereby strengthening risk assessment and management decision in wheat production in the south Atlantic region of the U.S.