Predictive Densities for Shire Level Wheat Yield in Western Australia

Wheat yield in Western Australia (WA) depends critically on rainfall during three periods – germination, growing and flowering. The degree of uncertainty attached to a wheat-yield prediction depends on whether the prediction is made before or after the rainfall in each period has been realised. Bayesian predictive densities that reflect the different levels of uncertainty in wheat-yield predictions made at four different points in time are derived for five shires in Western Australia. The framework used for prediction is a linear regression model with stochastic regressors and inequality restrictions on the coefficients. An algorithm is developed that can be used more generally for obtaining Bayesian predictive densities in linear and nonlinear models with inequality constraints, and with or without stochastic regressors.