Bayesian Analysis of Covariate-Driven Hawkes Processes with Application in Plant Epidemiology

Abstract

Hawkes processes are widely used to model temporal point patterns exhibiting self-exciting behavior. In this work, we consider a Hawkes model with a baseline intensity depending on a set of dynamic covariates and an exponential triggering function. A Bayesian approach is applied to variable selection in this context. Spike-and-slab priors are proposed to enable a parsimonious choice of relevant variables. We also provide practical simulation procedures for the fitted covariate-driven Hawkes model, which support posterior predictive checks and probabilistic forecasting. This approach is illustrated by the example of spore release of Venturia inaequalis, the fungus responsible for apple scab disease. We study the dependence of primary spore releases on environmental covariates and highlight the self-exciting behavior of subsequent releases. The Bayesian framework also provides a natural basis to forecast future spore releases. By delivering interpretable posterior inclusion probabilities alongside uncertainty-aware predictive risk bands, this new methodology provides a rigorous foundation for managing temporal event risks driven by both external environmental forcing and internal contagion.