Integrating Bayesian Inference and Supervised Learning for Predictive Modeling of Coffee Rust Incidence Among Kenyan Smallholder Farmers

Hemileia vastatrix a pathogenic fungus which causes coffee leaf rust, has been a significant challenge to the sustainability of Arabica coffee production in Kenya, where smallholder farmers experience frequent yield losses and lack access to effective control techniques. To manage it effectively, there is a need for predictive frameworks that quantify the risk and uncertainty of disease occurrence under real-world farm conditions. This research paper introduces a hybrid application model that combines both Bayesian hierarchical modelling and supervised machine learning to produce probabilistic predictions of coffee rust occurrence. The models were based on longitudinal data from 9,850 plots in six primary coffee-producing counties, in which microclimatic moisture — particularly leaf wetness duration and relative humidity were the key predictors of infection. Partial dependence and SHAP analyses provided evidence of nonlinear threshold effects: high humidity and extended leaf wetness significantly increased the likelihood of infection, and proximity to already infected farms amplified disease transmission. The most accurate predictive algorithm in the evaluated set was Logistic Regression, with the highest predictive accuracy (AUC-ROC = 0.867) and, at the same time, was interpretable and computationally efficient. The Bayesian hierarchical model also accounted for county-level heterogeneity and provided a robust measure of uncertainty. The findings, taken together, show that it is possible to develop a probabilistic modelling framework that can be replicated and interpreted to predict sustainable coffee disease. The proposed system provides a scalable, data-driven decision-support instrument to guide precision management plans and make smallholder coffee systems in Kenya and other tropical settings more resilient.