Conceptual frameworks for embedding ordinary differential equation models within Bayesian hierarchical modeling

Crop scientists are frequently interested in understanding how instantaneous biophysical processes integrate across a growing season to affect yield. Collecting repeated measurements of soil and crop variables over time is one way to quantify how these processes are affected by various environmental and climatic factors and how those effects integrate over time to produce yield. Combining these data with dynamic simulation models allow crop physiologists and modelers to characterize these responses. Traditionally, these models are built to be purely deterministic with a system of ordinary differential equations (ODEs) that describes how the system as a whole evolves over time. Within this approach, random aspects of the data generation process are generally relegated to a single error term, usually assumed to be normal and centered on 0. This presentation will describe recent work on embedding ODE models within a more robust modeling of the random components of the data generation process using Bayesian hierarchical modeling. The approach will be illustrated with an application to a winter wheat dataset and some potential conceptual frameworks for thinking about the interpretation of model terms will be presented.