Bayesian Approaches to Emulation for a Complex Computer Crop Yield Simulator with Mixed Inputs

Abstract

Agriculture is one area where the simulation of crop growth, nutrition, soil condition and pollution could be invaluable in any land management decisions. The Environmental Policy Integrated Climate Model (EPIC) is a simulation model to investigate the behaviour of crop yield in response to changes in inputs such as fertiliser levels, soil, steepness, and other environmental covariates. We build a model for crop yield around a non-linear Mitscherlich Baule growth model to make inferences about crop yield response to changes in continuous input and factor variables. A Bayesian hierarchical approach to the modelling was taken for mixed inputs, requiring Markov Chain Monte Carlo simulations to obtain samples from the posterior distributions, to validate and illustrate the results, and to carry out model selection.

The emulation of complex computer simulations has become an effective tool in exploring this high-dimensional simulated process's behaviour. Initially, we built a Bayes linear emulator to efficiently emulate crop yield as a function of the simulator's continuous inputs only. We explore emulator diagnostics and present the results from the emulation of a subset of the simulated EPIC data output. Computer models with quantitative inputs are used widely, but the challenge is incorporating the factors. We propose a framework for solving this issue considering the Bayes linear emulation approach. We explore a variety of correlation structures to represent the mixed inputs and combine this with the Bayes linear approach to construct an emulator. Finally, we developed a method to make an optimal decision for the farmers to gain maximum utility considering yield and pollutants, accounting for weather factors, land characteristics and fertiliser use.