A robust Bayesian land use model for crop rotations

Abstract

Often, in dynamical systems, such as farmers’ crop choices, the dynamics are driven by external non-stationary factors, such as rainfall and agricultural input and output prices. Such dynamics can be modelled by a non-stationary stochastic process, where the transition probabilities are functions of such external factors. We propose using a multinomial logit model for these transition probabilities, and investigate the problem of estimating the parameters of this model from data.

We adapt the work of Chen and Ibrahim to propose a conjugate prior distribution for the parameters of the multinomial logit model. Inspired by the imprecise Dirichlet model, we will perform a robust Bayesian analysis by proposing a fairly broad class of prior distributions, in order to accommodate scarcity of data and lack of strong prior expert opinion.

We discuss the computation of bounds for the posterior transition probabilities, using a variety of calculation methods. These sets of posterior transition probabilities
mean that our land use model consists of a non-stationary imprecise stochastic process. We discuss computation of future events in this process.

Finally, we use our novel land use model to investigate real-world data. We investigate the impact of external variables on the posterior transition probabilities, and investigate a scenario for future crop growth. We also use our model to solve a hypothetical yet realistic policy problem.